Dmitry E Pelinovsky - McMaster Experts

Affiliations

Faculty of Science, McMaster University
Professor, Mathematics and Statistics, Faculty of Science
Chair-of-Excellence Research Professor, University of Grenoble,
Humboldt Research Fellow, University of Stuttgart,
NATO Science Postdoctoral Fellow, University of Toronto,
Research Fellow, University of Cape Town,

Scholarly Activity in McMaster Experts

Co-author Network

Scholarly Activity
Teaching
Background
Contact
View All

selected scholarly activity

books
- Nonlinear Physical Systems. Ed. 9781848214200. 2013
- Localization in Periodic Potentials 2011
- Asymptotic methods in soliton stability theory. Ed. 12. 1997
chapters
- Traveling Waves in Fractional Models. 155-186. 2024
- Existence and Stability of Klein–Gordon Breathers in the Small-Amplitude Limit. Trends in Mathematics. 251-278. 2020
- Inverse Scattering for the Massive Thirring Model. Fields Institute Communications. 497-528. 2019
- Stability of Discrete Breathers in Magnetic Metamaterials. 359-374. 2014
- Asymptotic Reductions of the Gross-Pitaevskii Equation. 377-398. 2008
- Periodic oscillations of dark solitons in parabolic potentials. Contemporary Mathematics. 159-180. 2008
conferences
- On the uniform convergence of the Chebyshev interpolants for solitons. Mathematics and Computers in Simulation. 794-803. 2009
- Evans Function for the AKNS Problem with Algebraic Solitons. MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION, WAVES 2003. 729-734. 2003
- A mysterious threshold for transverse instability of deep-water solitons. Mathematics and Computers in Simulation. 585-594. 2001
- Nonlinear propagation of ultrashort pulses in nonlinear periodic materials with alternating oppositely-signed Kerr coefficients. Conference Proceedings - Lasers and Electro-Optics Society Annual Meeting-LEOS. 441-442. 2001
- OSCILLATORY INSTABILITY AND SUPERCRITICAL DYNAMICS OF DAMPED-DRIVEN NONLINEAR SCHRÖDINGER SOLITONS. Nonlinearity, Integrability and All That. 359-366. 2000
- Asymptotic approximations for a new eigenvalue in linear problems without a threshold. Theoretical and Mathematical Physics. 98-106. 2000
- Nonlinear Theory of Soliton Instabilities. PHYSICS AND APPLICATIONS OF OPTICAL SOLITONS IN FIBRES '95. 75-87. 1996
- On a structure of the explicit solutions to the Davey-Stewartson equations. Physica D : Non-linear phenomena. 115-122. 1995
- A set of travelling fronts of excitation in the model of homogeneous neuro-like medium with nonlocal coupling. [Proceedings] 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers. 855-864. 1992
- Formation of pulsed sources in neuro-like media. [Proceedings] 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers. 521-528. 1992
journal articles
- On the long-wave approximation of solitary waves in cylindrical coordinates. Nonlinear Differential Equations and Applications. 32:50. 2025
- Peaked Stokes waves as solutions of Babenko's equation. Applied Mathematics Letters. 161. 2025
- On smooth and peaked travelling waves in a local model for shallow water waves. Journal of Fluid Mechanics. 1004. 2025
- On the Existence of Generalized Breathers and Transition Fronts in Time-Periodic Nonlinear Lattices. SIAM Journal on Applied Dynamical Systems. 24:894-928. 2025
- Stability of Standing Periodic Waves in the Massive Thirring Model. Studies in Applied Mathematics. 154. 2025
- Turing Bifurcation in the Swift–Hohenberg Equation on Deterministic and Random Graphs. Journal of Nonlinear Science. 34. 2024
- Algebraic solitons in the massive Thirring model.. Physical Review E. 110:034202. 2024
- Stability of smooth periodic traveling waves in the Degasperis–Procesi equation. Journal of Differential Equations. 404:354-390. 2024
- Ground state of the Gross–Pitaevskii equation with a harmonic potential in the energy-critical case. Asymptotic Analysis. 139:1-29. 2024
- On the transverse stability of smooth solitary waves in a two-dimensional Camassa–Holm equation. Journal des Mathématiques Pures et Appliquées. 188:1-25. 2024
- Dark breathers on a snoidal wave background in the defocusing mKdV equation. Letters in Mathematical Physics. 114. 2024
- Pinning in the Extended Lugiato–Lefever Equation. SIAM Journal on Mathematical Analysis. 56:3679-3702. 2024
- Rogue waves arising on the standing periodic waves in the Ablowitz-Ladik equation (vol 152, pg 147, 2024). Studies in Applied Mathematics. 152:1478-1478. 2024
- Travelling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media. Nonlinearity. 37:055005-055005. 2024
- Stability of Black Solitons in Optical Systems with Intensity-Dependent Dispersion. SIAM Journal on Mathematical Analysis. 56:2521-2568. 2024
- Bright and dark breathers of the Benjamin–Ono equation on the traveling periodic background. Wave Motion. 126:103263-103263. 2024
- Dynamics of the black soliton in a regularized nonlinear Schrödinger equation. Proceedings of the American Mathematical Society. 152:1217-1231. 2024
- On the Extinction of Multiple Shocks in Scalar Viscous Conservation Laws. SIAM Journal on Applied Dynamical Systems. 23:2323-2363. 2024
- Rogue waves arising on the standing periodic waves in the Ablowitz–Ladik equation. Studies in Applied Mathematics. 152:147-173. 2024
- Positive solutions of the Gross–Pitaevskii equation for energy critical and supercritical nonlinearities. Nonlinearity. 36:3684-3709. 2023
- KdV breathers on a cnoidal wave background. Journal of Physics A: Mathematical and Theoretical. 56:185701-185701. 2023
- Periodic waves in the discrete mKdV equation: Modulational instability and rogue waves. Physica D : Non-linear phenomena. 445:133652-133652. 2023
- KP-II Approximation for a Scalar Fermi–Pasta–Ulam System on a 2D Square Lattice. SIAM Journal on Applied Mathematics. 83:79-98. 2023
- Extinction of multiple shocks in the modular Burgers’ equation. Nonlinear Dynamics. 111:3679-3687. 2023
- Rogue waves in the sea: observations, physics, and mathematics. Physics-Uspekhi. 66:148-172. 2023
- Periodic Waves of the Modified KdV Equation as Minimizers of a New Variational Problem. SIAM Journal on Applied Dynamical Systems. 21:2518-2534. 2022
- Morse index for the ground state in the energy supercritical Gross–Pitaevskii equation. Journal of Differential Equations. 341:380-401. 2022
- Solitons on the rarefaction wave background via the Darboux transformation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 478. 2022
- Stability of smooth solitary waves in the b-Camassa–Holm equation. Physica D : Non-linear phenomena. 440:133477-133477. 2022
- Domain walls in the coupled Gross–Pitaevskii equations with the harmonic potential. Calculus of Variations and Partial Differential Equations. 61. 2022
- Justification of the KP-II approximation in dynamics of two-dimensional FPU systems. Zeitschrift für Angewandte Mathematik und Physik. 73. 2022
- Linear Instability of Breathers for the Focusing Nonlinear Schrödinger Equation. Journal of Nonlinear Science. 32. 2022
- Spectral Instability of Peakons in the $b$-Family of the Camassa--Holm Equations. SIAM Journal on Mathematical Analysis. 54:4572-4590. 2022
- Standing waves on quantum graphs. Journal of Physics A: Mathematical and Theoretical. 55:243001-243001. 2022
- Correction to: Periodic Waves in the Fractional Modified Korteweg–de Vries Equation. Journal of Dynamics and Differential Equations. 34:1641-1642. 2022
- Periodic Waves in the Fractional Modified Korteweg–de Vries Equation. Journal of Dynamics and Differential Equations. 34:1601-1640. 2022
- Stability of smooth periodic travelling waves in the Camassa–Holm equation. Studies in Applied Mathematics. 148:27-61. 2022
- Multi-pulse edge-localized states on quantum graphs. Analysis and Mathematical Physics. 11. 2021
- Solitary waves with intensity-dependent dispersion: variational characterization. Journal of Physics A: Mathematical and Theoretical. 54:445701-445701. 2021
- Edge-localized states on quantum graphs in the limit of large mass. Annales de l'Institut Henri Poincare. Analyse non linéar. 38:1295-1335. 2021
- Green’s Function for the Fractional KDV Equation on the Periodic Domain via Mittag-Leffler Function. Fractional Calculus and Applied Analysis. 24:1507-1534. 2021
- Stability and interaction of compactons in the sublinear KdV equation. Communications in Nonlinear Science and Numerical Simulation. 101:105855-105855. 2021
- Asymptotic stability of viscous shocks in the modular Burgers equation. Nonlinearity. 34:5979-6016. 2021
- Ground state in the energy super-critical Gross–Pitaevskii equation with a harmonic potential. Nonlinear Analysis, Theory, Methods and Applications. 210:112358-112358. 2021
- Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation. Journal of Nonlinear Science. 31. 2021
- Rogue waves on the background of periodic standing waves in the derivative nonlinear Schrödinger equation. Physical Review E. 103:062206. 2021
- Localization in optical systems with an intensity-dependent dispersion. Quarterly of Applied Mathematics. 79:641-665. 2021
- Rogue waves in the KdV-type models 2021
- Instability of Double-Periodic Waves in the Nonlinear Schrödinger Equation. Frontiers in Physics. 9. 2021
- Book Review: Nonlinear Dirac equations: Spectral stability of solitary waves. Bulletin of the American Mathematical Society. 58:289-294. 2021
- $W^{1,\infty}$ instability of $H^1$-stable peakons in the Novikov equation. Dynamics of Partial Differential Equations. 18:176-197. 2021
- W^1,∞ instability of H¹-stable peakons in the Novikov equation. Dynamics of Partial Differential Equations. 18:173-197. 2021
- Growth of Perturbations to the Peaked Periodic Waves in the Camassa--Holm Equation. SIAM Journal on Mathematical Analysis. 53:3016-3039. 2021
- Standing waves on a flower graph. Journal of Differential Equations. 271:719-763. 2021
- Localized structures on librational and rotational travelling waves in the sine-Gordon equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 476. 2020
- Standing waves of the quintic NLS equation on the tadpole graph. Calculus of Variations and Partial Differential Equations. 59. 2020
- Observation of modulation instability and rogue breathers on stationary periodic waves. Physical Review Research. 2. 2020
- Spectral instability of the peaked periodic wave in the reduced Ostrovsky equations. Proceedings of the American Mathematical Society. 148:5109-5125. 2020
- The monoatomic FPU system as a limit of a diatomic FPU system. Applied Mathematics Letters. 107:106387-106387. 2020
- Chern–Simons–Schrödinger theory on a one-dimensional lattice. Letters in Mathematical Physics. 110:2221-2244. 2020
- Instability of H1-stable peakons in the Camassa–Holm equation. Journal of Differential Equations. 268:7342-7363. 2020
- New variational characterization of periodic waves in the fractional Korteweg–de Vries equation. Nonlinearity. 33:1956-1986. 2020
- Periodic standing waves in the focusing nonlinear Schrödinger equation: Rogue waves and modulation instability. Physica D : Non-linear phenomena. 405:132378-132378. 2020
- Bifurcation of nonlinear bound states in the periodic Gross-Pitaevskii equation with ��-symmetry. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 150:171-204. 2020
- Stationary states of the cubic conformal flow on <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{S}^3 $\end{document}</tex-math></inline-formula>. Discrete and Continuous Dynamical Systems. Series A. 40:1-32. 2020
- Periodic Travelling Waves of the Modified KdV Equation and Rogue Waves on the Periodic Background. Journal of Nonlinear Science. 29:2797-2843. 2019
- Darboux transformation and soliton solutions of the semi-discrete massive Thirring model. Physics Letters, Section A: General, Atomic and Solid State Physics. 383:125948-125948. 2019
- Rogue waves on the double-periodic background in the focusing nonlinear Schrödinger equation. Physical Review E. 100:052219. 2019
- Standing lattice solitons in the discrete NLS equation with saturation. Nonlinearity. 32:3445-3484. 2019
- Ground State of the Conformal Flow on �³. Communications on Pure and Applied Mathematics. 72:1123-1151. 2019
- Nonexistence of self-similar blowup for the nonlinear Dirac equations in (1+1) dimensions. Applied Mathematics Letters. 92:176-183. 2019
- Preface: Nonlinear waves in fluids in honor of Roger Grimshaw on the occasion of his 80th birthday: Part II. Studies in Applied Mathematics. 142:417-418. 2019
- Preface: Nonlinear waves in fluids in honor of Roger Grimshaw on the occasion of his 80th birthday. Studies in Applied Mathematics. 142:215-218. 2019
- Integrable semi-discretization of the massive Thirring system in laboratory coordinates. Journal of Physics A: Mathematical and Theoretical. 52:03LT01-03LT01. 2019
- Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation. SIAM Journal on Mathematical Analysis. 51:2850-2883. 2019
- Convergence of Petviashvili's method near periodic waves in the fractional Korteweg-de Vries equation. SIAM Journal on Mathematical Analysis. 51:2850-2883. 2019
- Drift of Spectrally Stable Shifted States on Star Graphs. SIAM Journal on Applied Dynamical Systems. 18:1723-1755. 2019
- Inverse Scattering for the Massive Thirring Model. Fields Institute Communications. 83:497-528. 2019
- Linear Instability and Uniqueness of the Peaked Periodic Wave in the Reduced Ostrovsky Equation. SIAM Journal on Mathematical Analysis. 51:1188-1208. 2019
- Helical solitons in vector modified Korteweg–de Vries equations. Physics Letters, Section A: General, Atomic and Solid State Physics. 382:3165-3171. 2018
- On the impossibility of solitary Rossby waves in meridionally unbounded domains. Physics of Fluids. 30. 2018
- Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption. Nonlinearity. 31:4621-4648. 2018
- Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method. International mathematics research notices. 2018:5663-5728. 2018
- Nonlinear instability of half-solitons on star graphs. Journal of Differential Equations. 264:7357-7383. 2018
- Krein signature for instability of PT-symmetric states. Physica D : Non-linear phenomena. 371:48-59. 2018
- Rogue periodic waves of the modified KdV equation. Nonlinearity. 31:1955-1980. 2018
- Nonlinear Partial Differential Equations on Graphs. Oberwolfach Reports. 14:1805-1868. 2018
- Spectral stability of shifted states on star graphs. Journal of Physics A: Mathematical and Theoretical. 51:095203-095203. 2018
- Rogue periodic waves of the focusing nonlinear Schrödinger equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 474:20170814-20170814. 2018
- Rogue periodic waves of the focusing nonlinear Schrödinger equation.. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 474:20170814. 2018
- Krein Signature in Hamiltonian and P T $$\mathbb {PT}$$ -Symmetric Systems. Springer Tracts in Modern Physics. 280:465-491. 2018
- Normal form for transverse instability of the line soliton with a nearly critical speed of propagation. Mathematical Modelling of Natural Phenomena. 13:23-23. 2018
- Orbital Stability of Domain Walls in Coupled Gross--Pitaevskii Systems. SIAM Journal on Mathematical Analysis. 50:810-833. 2018
- Bifurcations of Multi-Vortex Configurations in Rotating Bose–Einstein Condensates. Milan Journal of Mathematics. 85:331-367. 2017
- Coupled pendula chains under parametricPT-symmetric driving force. Physics Letters, Section A: General, Atomic and Solid State Physics. 381:3884-3892. 2017
- On the characterization of vortex configurations in the steady rotating Bose–Einstein condensates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 473:20170602-20170602. 2017
- Counting Unstable Eigenvalues in Hamiltonian Spectral Problems via Commuting Operators. Communications in Mathematical Physics. 354:247-268. 2017
- Global solutions to the shallow water system with a method of an additional argument. Applicable Analysis. 96:1444-1465. 2017
- Spectral stability of periodic waves in the generalized reduced Ostrovsky equation. Letters in Mathematical Physics. 107:1293-1314. 2017
- Ground state of the conformal flow on $\mathbb{S}^3$ 2017
- New integrable semi-discretizations of the coupled nonlinear Schrodinger equations 2017
- Bifurcations of Standing Localized Waves on Periodic Graphs. Annales Henri Poincare. 18:1185-1211. 2017
- Long-time stability of small FPU solitary waves. Discrete and Continuous Dynamical Systems. Series A. 37:2065-2075. 2017
- On the linearized log-KdV equation. Communications in Mathematical Sciences. 15:863-880. 2017
- The derivative NLS equation: global existence with solitons. Dynamics of Partial Differential Equations. 14:271-294. 2017
- Validity of the NLS approximation for periodic quantum graphs. Nonlinear Differential Equations and Applications. 23. 2016
- Long-time stability of breathers in Hamiltonian ${ \mathcal P }{ \mathcal T }$-symmetric lattices. Journal of Physics A: Mathematical and Theoretical. 49:475201-475201. 2016
- Orbital stability of periodic waves in the class of reduced Ostrovsky equations. Journal of Differential Equations. 261:3268-3304. 2016
- Energy Criterion for the Spectral Stability of Discrete Breathers. Physical Review Letters. 117:094101. 2016
- Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrödinger equations. Reviews in Mathematical Physics. 28:1650015-1650015. 2016
- Nonlinear Instabilities of Multi‐Site Breathers in Klein–Gordon Lattices. Studies in Applied Mathematics. 137:214-237. 2016
- Breathers in Hamiltonian PT -Symmetric Chains of Coupled Pendula under a Resonant Periodic Force. Symmetry. 8:59-59. 2016
- Existence and stability of PT-symmetric states in nonlinear two-dimensional square lattices. Physica D : Non-linear phenomena. 326:1-20. 2016
- Transverse Instability of Line Solitary Waves in Massive Dirac Equations. Journal of Nonlinear Science. 26:365-403. 2016
- Global solutions to the shallow-water system 2016
- L²orbital stability of Dirac solitons in the massive Thirring model. Communications in Partial Differential Equations. 41:227-255. 2016
- Ground State on the Dumbbell Graph. Applied Mathematics Research eXpress. 2016:98-145. 2016
- Self-Similar Solutions for Reversing Interfaces in the Slow Diffusion Equation with Strong Absorption. SIAM Journal on Applied Dynamical Systems. 15:2017-2050. 2016
- Global Existence of Solutions to Coupled � � $\mathcal {PT}$ -Symmetric Nonlinear Schrödinger Equations. International Journal of Theoretical Physics. 54:3920-3931. 2015
- Dimer with gain and loss: Integrability and ${\mathcal{P}}{\mathcal{T}}$-symmetry restoration. Journal of Physics A: Mathematical and Theoretical. 48:325201-325201. 2015
- Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph. Nonlinearity. 28:2343-2378. 2015
- On numerical modelling and the blow-up behavior of contact lines with a $$\mathbf{180}^{\varvec{\circ }}$$ 180 ∘ contact angle. Journal of Engineering Mathematics. 92:31-44. 2015
- When Linear Stability Does Not Exclude Nonlinear Instability. Physical Review Letters. 114:214101. 2015
- Orbital stability in the cubic defocusing NLS equation: I. Cnoidal periodic waves. Journal of Differential Equations. 258:3607-3638. 2015
- Orbital stability in the cubic defocusing NLS equation: II. The black soliton. Journal of Differential Equations. 258:3639-3660. 2015
- Domain Walls in the Coupled Gross–Pitaevskii Equations. Archive for Rational Mechanics and Analysis. 215:579-610. 2015
- Persistence of the Thomas–Fermi approximation for ground states of the Gross–Pitaevskii equation supported by the nonlinear confinement. Applied Mathematics Letters. 40:45-48. 2015
- On the orbital stability of Gaussian solitary waves in the log-KdV equation. Nonlinearity. 27:3185-3202. 2014
- On the Thomas–Fermi Approximation of the Ground State in a ‐Symmetric Confining Potential. Studies in Applied Mathematics. 133:398-421. 2014
- Persistence of the Thomas-Fermi approximation for ground states supported by the nonlinear confinement 2014
- Validity of the Weakly Nonlinear Solution of the Cauchy Problem for the Boussinesq‐Type Equation. Studies in Applied Mathematics. 133:52-83. 2014
- Justification of a nonlinear Schrödinger model for laser beams in photopolymers. Zeitschrift für Angewandte Mathematik und Physik. 65:405-433. 2014
- Lattice Differential Equations. Oberwolfach Reports. 10:2631-2689. 2014
- Stability of multi-solitons in the cubic NLS equation. Journal of Hyperbolic Differential Equations. 11:329-353. 2014
- Gaussian solitary waves and compactons in Fermi–Pasta–Ulam lattices with Hertzian potentials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 470:20130462-20130462. 2014
- Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation. Theoretical and Mathematical Physics. 179:452-461. 2014
- The asymptotic stability of solitons in the cubic NLS equation on the line. Applicable Analysis. 93:791-822. 2014
- Nonlinear modes in a generalized $\mathcal{PT}$-symmetric discrete nonlinear Schrödinger equation. Journal of Physics A: Mathematical and Theoretical. 47:085204-085204. 2014
- Wave Systems with an Infinite Number of Localized Traveling Waves. Physical Review Letters. 112:054103. 2014
- Justification of the log--KdV Equation in Granular Chains: The Case of Precompression. SIAM Journal on Mathematical Analysis. 46:4075-4103. 2014
- Orbital Stability of Dirac Solitons. Letters in Mathematical Physics. 104:21-41. 2014
- Preface. International Review of Cell and Molecular Biology. 307:xiii-xiii. 2014
- Spectral Stability of Nonlinear Waves in KdV‐Type Evolution Equations 2013
- Periodic Traveling Waves in Diatomic Granular Chains. Journal of Nonlinear Science. 23:689-730. 2013
- Universal power law for the energy spectrum of breaking Riemann waves. Journal of Experimental and Theoretical Physics. 98:237-241. 2013
- Nonlinear dynamics in PT-symmetric lattices. Journal of Physics A: Mathematical and Theoretical. 46:365201-365201. 2013
- On numerical modelling of contact lines in fluid flows 2013
- Global existence of small-norm solutions in the reduced Ostrovsky equation. Discrete and Continuous Dynamical Systems. Series A. 34:557-566. 2013
- Multilevel computations of dispersed drug release. Numerical Methods for Partial Differential Equations. 29:1391-1415. 2013
- On transverse stability of discrete line solitons. Physica D : Non-linear phenomena. 255:1-11. 2013
- Matter-Wave Bright Solitons in Spin-Orbit Coupled Bose-Einstein Condensates. Physical Review Letters. 110:264101. 2013
- Rigorous justification of the short-pulse equation. Nonlinear Differential Equations and Applications. 20:1277-1294. 2013
- Finite-time singularities in the dynamical evolution of contact lines 2013
- On solutions of the reduced model for the dynamical evolution of contact lines 2013
- Bifurcations of Asymmetric Vortices in Symmetric Harmonic Traps. Applied Mathematics Research eXpress. 2013:127-164. 2013
- Nonlinear Stationary States in PT-Symmetric Lattices. SIAM Journal on Applied Dynamical Systems. 12:1210-1236. 2013
- \chem{\mathcal {P}\mathcal {T}} -symmetric lattices with spatially extended gain/loss are generically unstable. Europhysics Letters. 101:11002-11002. 2013
- Discrete solitons in \chem {\cal PT} -symmetric lattices. Europhysics Letters. 100:56006-56006. 2012
- Multi-site breathers in Klein–Gordon lattices: stability, resonances and bifurcations. Nonlinearity. 25:3423-3451. 2012
- Sharp bounds on enstrophy growth in the viscous Burgers equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 468:3636-3648. 2012
- Normal form for the symmetry-breaking bifurcation in the nonlinear Schrödinger equation. Journal of Differential Equations. 253:2796-2824. 2012
- Asymptotic stability of small gap solitons in nonlinear Dirac equations. Journal of Mathematical Physics. 53. 2012
- Loops of Energy Bands for Bloch Waves in Optical Lattices. Studies in Applied Mathematics. 128:300-336. 2012
- Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential. Physical Review E. 85:026605. 2012
- Backlund Transformation and L2-stability of NLS Solitons. International mathematics research notices. 2012:2034-2067. 2012
- Breather continuation from infinity in nonlinear oscillator chains. Discrete and Continuous Dynamical Systems. Series A. 32:1775-1799. 2012
- Enstrophy growth in the viscous Burgers equation. Dynamics of Partial Differential Equations. 9:305-340. 2012
- On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - Series S. 5:971-987. 2012
- On the validity of the variational approximation in discrete nonlinear Schrödinger equations. Physica D : Non-linear phenomena. 241:115-124. 2012
- Polychromatic Solitary Waves in a Periodic and Nonlinear Maxwell System. SIAM Journal on Applied Dynamical Systems. 11:478-506. 2012
- Preface. Discrete and Continuous Dynamical Systems - Series S. 5:i-iii. 2012
- Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows. Physical Review E. 84:065301. 2011
- Symmetry-Breaking Bifurcation in the Nonlinear Schrödinger Equation with Symmetric Potentials. Communications in Mathematical Physics. 308:795-844. 2011
- Propagation failure in the discrete Nagumo equation. Proceedings of the American Mathematical Society. 139:3537-3537. 2011
- Regularized shock solutions in coating flows with small surface tension. Physics of Fluids. 23. 2011
- Convergence of the Adomian decomposition method for initial-value problems. Numerical Methods for Partial Differential Equations. 27:749-766. 2011
- Broad Band Solitons in a Periodic and Nonlinear Maxwell System 2011
- Variational approximations of trapped vortices in the large-density limit. Nonlinearity. 24:1271-1289. 2011
- Traveling Monotonic Fronts in the Discrete Nagumo Equation. Journal of Dynamics and Differential Equations. 23:167-183. 2011
- Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation. Physica D : Non-linear phenomena. 240:265-281. 2011
- Asymptotic behavior of regularized shock solutions in coating flows 2011
- On the Thomas–Fermi ground state in a harmonic potential. Asymptotic Analysis. 73:53-96. 2011
- Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonlinear Schrödinger lattices. Discrete and Continuous Dynamical Systems - Series S. 4:1019-1031. 2011
- Effects of rotation on stability of viscous stationary flows on a spherical surface. Physics of Fluids. 22. 2010
- Homogenization of the variable-speed wave equation. Wave Motion. 47:496-507. 2010
- Survey on global existence in the nonlinear Dirac equations in one dimension 2010
- Asymptotic properties of excited states in the Thomas–Fermi limit. Nonlinear Analysis, Theory, Methods and Applications. 73:2631-2643. 2010
- Bifurcation of gap solitons in periodic potentials with a periodic sign-varying nonlinearity coefficient. Applicable Analysis. 89:1335-1350. 2010
- Excited states in the large density limit: a variational approach. Nonlinearity. 23:1753-1770. 2010
- Count of eigenvalues in the generalized eigenvalue problem. Journal of Mathematical Physics. 51. 2010
- Global Well-Posedness of the Short-Pulse and Sine–Gordon Equations in Energy Space. Communications in Partial Differential Equations. 35:613-629. 2010
- Bounds on the tight-binding approximation for the Gross–Pitaevskii equation with a periodic potential. Journal of Differential Equations. 248:837-849. 2010
- Distribution of eigenfrequencies for oscillations of the ground state in the Thomas-Fermi limit. Physical Review A (PRA). 81. 2010
- Wave Breaking in the Ostrovsky–Hunter Equation. SIAM Journal on Mathematical Analysis. 42:1967-1985. 2010
- On quadratic eigenvalue problems arising in stability of discrete vortices. Linear Algebra and Its Applications. 431:962-973. 2009
- Eigenvalues of a nonlinear ground state in the Thomas–Fermi approximation. Journal of Mathematical Analysis and Applications. 355:495-526. 2009
- Coupled-Mode Equations and Gap Solitons in a Two-Dimensional Nonlinear Elliptic Problem with a Separable Periodic Potential. Journal of Nonlinear Science. 19:95-131. 2009
- Incompressible Viscous Fluid Flows in a Thin Spherical Shell. Journal of Mathematical Fluid Mechanics. 11:60-90. 2009
- Asymptotic Stability of Small Bound States in the Discrete Nonlinear Schrödinger Equation. SIAM Journal on Mathematical Analysis. 41:2010-2030. 2009
- Discrete Traveling Solitons in the Salerno Model. SIAM Journal on Applied Dynamical Systems. 8:689-709. 2009
- Wave breaking in the short-pulse equation. Dynamics of Partial Differential Equations. 6:291-310. 2009
- Justification of the Lattice Equation for a Nonlinear Elliptic Problem with a Periodic Potential. Communications in Mathematical Physics. 284:803-831. 2008
- Slow-light dispersion in coupled periodic waveguides. Journal of the Optical Society of America. B, Optical physics. 25:C65-C65. 2008
- Three-dimensional gravity waves in a channel of variable depth. Communications in Nonlinear Science and Numerical Simulation. 13:2104-2113. 2008
- On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension. Journal of Mathematical Physics. 49. 2008
- Asymptotic stability of small solitons in the discrete nonlinear Schrodinger equation in one dimension 2008
- Moving gap solitons in periodic potentials. Mathematical Methods in the Applied Sciences. 31:1739-1760. 2008
- Dark solitons in external potentials. Zeitschrift für Angewandte Mathematik und Physik. 59:559-599. 2008
- Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations. Journal of Mathematical Sciences. 151:3091-3111. 2008
- Periodic oscillations of discrete NLS solitons in the presence of diffraction management. Nonlinearity. 21:1265-1279. 2008
- Spectrum of a non-self-adjoint operator associated with the periodic heat equation. Journal of Mathematical Analysis and Applications. 342:970-988. 2008
- Stability of discrete dark solitons in nonlinear Schrödinger lattices. Journal of Physics A: Mathematical and Theoretical. 41:185206-185206. 2008
- Lyapunov–Schmidt reduction algorithm for three-dimensional discrete vortices. Physica D : Non-linear phenomena. 237:339-350. 2008
- Periodic oscillations of dark solitons in parabolic potentials. Contemporary Mathematics. 473:159-+. 2008
- Surface Gap Solitons at a Nonlinearity Interface. SIAM Journal on Applied Dynamical Systems. 7:249-264. 2008
- One-parameter localized traveling waves in nonlinear Schrödinger lattices. Physica D : Non-linear phenomena. 236:22-43. 2007
- Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential. Applicable Analysis. 86:1017-1036. 2007
- Nonlinear Instability of a Critical Traveling Wave in the Generalized Korteweg–de Vries Equation. SIAM Journal on Mathematical Analysis. 39:1-33. 2007
- Two-pulse solutions in the fifth-order KdV equation: Rigorous theory and numerical approximations. Discrete and Continuous Dynamical Systems - Series B. 8:773-800. 2007
- Translationally invariant nonlinear Schrödinger lattices. Nonlinearity. 19:2695-2716. 2006
- Exact conditions for existence of homoclinic orbits in the fifth-order KdV model. Nonlinearity. 19:2277-2312. 2006
- Discrete vector on-site vortices. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 462:2671-2694. 2006
- Feshbach resonance management of Bose-Einstein condensates in optical lattices. Physical Review E. 74:036610. 2006
- Transverse instabilities of deep-water solitary waves. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 462:2039-2061. 2006
- Eigenvalues of zero energy in the linearized NLS problem. Journal of Mathematical Physics. 47. 2006
- Normal form for travelling kinks in discrete Klein–Gordon lattices. Physica D : Non-linear phenomena. 216:327-345. 2006
- Evans Function for Lax Operators with Algebraically Decaying Potentials. Journal of Nonlinear Science. 16:1-44. 2006
- Nonlinearity management in higher dimensions. Journal of Physics A: Mathematical and Theoretical. 39:479-488. 2006
- Block-Diagonalization of the Symmetric First-Order Coupled-Mode System. SIAM Journal on Applied Dynamical Systems. 5:66-83. 2006
- Parametric resonance of ground states in the nonlinear Schrödinger equation. Journal of Differential Equations. 220:85-120. 2006
- Travelling kinks in discrete phi⁴models. Nonlinearity. 19:217-235. 2006
- Persistence and stability of discrete vortices in nonlinear Schrödinger lattices. Physica D : Non-linear phenomena. 212:20-53. 2005
- Stability of discrete solitons in nonlinear Schrödinger lattices. Physica D : Non-linear phenomena. 212:1-19. 2005
- Averaging of nonlinearity-managed pulses. Chaos. 15:37105. 2005
- Solitons in nonintegrable systems. Chaos. 15:37101. 2005
- Stability analysis of embedded solitons in the generalized third-order nonlinear Schrödinger equation. Chaos. 15:37115. 2005
- Translationally invariant discrete kinks from one-dimensional maps. Physical Review E. 72:035602. 2005
- Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers. Studies in Applied Mathematics. 115:157-171. 2005
- Spectral stability and time evolution ofN-solitons in the KdV hierarchy. Journal of Physics A: Mathematical and Theoretical. 38:6129-6140. 2005
- Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations. Studies in Applied Mathematics. 115:109-137. 2005
- Oscillations of dark solitons in trapped Bose-Einstein condensates. Physical Review E. 72:016615. 2005
- Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrödinger problem. Journal of Mathematical Physics. 46. 2005
- Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 461:783-812. 2005
- Bifurcations of travelling wave solutions in the discrete NLS equations. Physica D : Non-linear phenomena. 202:16-36. 2005
- Modeling of Wave Resonances in Low-Contrast Photonic Crystals. SIAM Journal on Applied Mathematics. 65:1101-1129. 2005
- Spectra of positive and negative energies in the linearized NLS problem. Communications on Pure and Applied Mathematics. 58:1-29. 2005
- Nonlinear Schrödinger lattices II: Persistence and Stability of Discrete Vortices 2004
- Nonlinear Schrödinger lattices I: Stability of discrete solitons 2004
- Hamiltonian averaging for solitons with nonlinearity management. Physical Review E. 70:047604. 2004
- Bifurcations and stability of gap solitons in periodic potentials. Physical Review E. 70:036618. 2004
- Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations. SIAM Journal on Numerical Analysis. 42:1110-1127. 2004
- Parametric Resonance and Radiative Decay of Dispersion-Managed Solitons. SIAM Journal on Applied Mathematics. 64:1360-1382. 2004
- Averaging for Solitons with Nonlinearity Management. Physical Review Letters. 91:240201. 2003
- Purely nonlinear instability of standing waves with minimal energy. Communications on Pure and Applied Mathematics. 56:1565-1607. 2003
- Stability Analysis of Stationary Light Transmission in Nonlinear Photonic Structures. Journal of Nonlinear Science. 13:347-396. 2003
- On the exchange of energy in coupled Klein–Gordon equations. Wave Motion. 38:1-10. 2003
- Gauge transformation and spectral decomposition for the Ishimori-II equations. Journal of Physics A: Mathematical and Theoretical. 36:5557-5574. 2003
- Stable all-optical limiting in nonlinear periodic structures III Nonsolitonic pulse propagation. Journal of the Optical Society of America. B, Optical physics. 20:695-695. 2003
- Averaging of Dispersion-Managed Solitons: Existence and Stability. SIAM Journal on Applied Mathematics. 63:745-776. 2003
- Stable vortex and dipole vector solitons in a saturable nonlinear medium. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 67:166081-1660812. 2003
- Stable vortex and dipole vector solitons in a saturable nonlinear medium. Physical Review E. 67:016608. 2003
- Generation of large-amplitude solitons in the extended Korteweg–de Vries equation. Chaos. 12:1070-1076. 2002
- Depletion layer and contact capacitance in non-uniformly doped semiconductors. Journal of Physics D: Applied Physics. 35:2988-2993. 2002
- Semi-stability of embedded solitons in the general fifth-order KdV equation. Wave Motion. 36:241-255. 2002
- Stable all-optical limiting in nonlinear periodic structures II Computations. Journal of the Optical Society of America. B, Optical physics. 19:1873-1873. 2002
- A normal form for nonlinear resonance of embedded solitons. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 458:1469-1497. 2002
- Stable all-optical limiting in nonlinear periodic structures I Analysis. Journal of the Optical Society of America. B, Optical physics. 19:43-43. 2002
- Wave group dynamics in weakly nonlinear long-wave models. Physica D : Non-linear phenomena. 159:35-57. 2001
- Charged-Particle Pseudorapidity Density Distributions fromAu+AuCollisions atsNN=130GeV. Physical Review Letters. 87:102303. 2001
- Transverse Instability of Vector Solitons and Generation of Dipole Arrays. Physical Review Letters. 87:103903. 2001
- Interaction of lumps with a line soliton for the DSII equation. Physica D : Non-linear phenomena. 152-153:189-198. 2001
- Stability criterion for multicomponent solitary waves. Physical Review E. 62:8668-8676. 2000
- Stability criterion for multicomponent solitary waves.. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 62:8668-8676. 2000
- Internal Oscillations and Radiation Damping of Vector Solitons. Studies in Applied Mathematics. 105:245-276. 2000
- Transmission regimes of periodic nonlinear optical structures. Physical Review E. 62:R4536-R4539. 2000
- Instabilities of dispersion-managed solitons in the normal dispersion regime. Physical Review E. 62:4283-4293. 2000
- Persistent oscillations of scalar and vector dispersion-managed solitons. Chaos. 10:539-550. 2000
- Self-focusing and transverse instabilities of solitary waves. Physics reports. 331:117-195. 2000
- Spectral decomposition for the Dirac system associated to the DSII equation. Inverse Problems. 16:59-74. 2000
- Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering. Communications in Mathematical Physics. 208:713-760. 2000
- Асимптотики нового собственного значения в линейных задачах без порога. Theoretical and Mathematical Physics. 122:118-127. 2000
- Generation of soliton oscillations in nonlinear quadratic materials. Physical Review E. 59:7250-7253. 1999
- Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability. Nonlinearity. 12:103-140. 1999
- Bifurcations of new eigenvalues for the Benjamin–Ono equation. Journal of Mathematical Physics. 39:6552-6572. 1998
- Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions. Journal of Mathematical Physics. 39:5377-5395. 1998
- Exact vortex solutions of the complex sine-Gordon theory on the plane. Physics Letters B. 436:117-124. 1998
- Radiative effects to the adiabatic dynamics of envelope-wave solitons. Physica D : Non-linear phenomena. 119:301-313. 1998
- Internal Modes of Solitary Waves. Physical Review Letters. 80:5032-5035. 1998
- Vibrations and Oscillatory Instabilities of Gap Solitons. Physical Review Letters. 80:5117-5120. 1998
- Internal modes of envelope solitons. Physica D : Non-linear phenomena. 116:121-142. 1998
- On internal wave–shear flow resonance in shallow water. Journal of Fluid Mechanics. 354:209-237. 1998
- On modified NLS, Kaup and NLBq equations: differential transformations and bilinearization. Journal of Physics A: Mathematical and Theoretical. 30:8705-8717. 1997
- Instability analysis of internal solitary waves in a nearly uniformly stratified fluid. Physics of Fluids. 9:3343-3352. 1997
- Structural transformation of eigenvalues for a perturbed algebraic soliton potential. Physics Letters, Section A: General, Atomic and Solid State Physics. 229:165-172. 1997
- An asymptotic approach to solitary wave instability and critical collapse in long-wave KdV-type evolution equations. Physica D : Non-linear phenomena. 98:139-155. 1996
- Non local Models for Envelope Waves in a Stratified Fluid. Studies in Applied Mathematics. 97:369-391. 1996
- Instability-induced dynamics of dark solitons. Physical Review E. 54:2015-2032. 1996
- On the asymptotic integrability of a higher-order evolution equation describing internal waves in a deep fluid. Journal of Mathematical Physics. 37:3415-3421. 1996
- Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation. Physical Review E. 53:1940-1953. 1996
- GENERATION OF COLLECTIVE-ACTIVITY STRUCTURES IN A HOMOGENEOUS NEURON-LIKE MEDIUM I: BIFURCATION ANALYSIS OF STATIC STRUCTURES. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 06:81-87. 1996
- GENERATION OF COLLECTIVE-ACTIVITY STRUCTURES IN A HOMOGENEOUS NEURON-LIKE MEDIUM II: DYNAMICS OF PROPAGATING AND PULSATING STRUCTURES. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 06:89-100. 1996
- Collapse transformation for self-focusing solitary waves in boundary-layer type shear flows. Physics Letters, Section A: General, Atomic and Solid State Physics. 206:195-202. 1995
- A spectral transform for the intermediate nonlinear Schrödinger equation. Journal of Mathematical Physics. 36:4203-4219. 1995
- Asymptotic theory of plane soliton self-focusing in two-dimensional wave media. Physica D : Non-linear phenomena. 85:468-484. 1995
- Instability of Solitons Governed by Quadratic Nonlinearities. Physical Review Letters. 75:591-595. 1995
- On a wave field transformation described by the two-dimensional Kadomtsev-Petviashvili equation. Inverse Problems. 11:603-610. 1995
- Self-focusing of plane dark solitons in nonlinear defocusing media. Physical Review E. 51:5016-5026. 1995
- Intermediate nonlinear Schrödinger equation for internal waves in a fluid of finite depth. Physics Letters, Section A: General, Atomic and Solid State Physics. 197:401-406. 1995
- The structure of the rational solutions to the Boussinesq equation. Physica D : Non-linear phenomena. 80:246-255. 1995
- Instability and decay of solitary waves in the Davey-Stewartson 1 system. Physics Letters, Section A: General, Atomic and Solid State Physics. 196:181-186. 1994
- Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution. Journal of Mathematical Physics. 35:5820-5830. 1994
- Stability of smooth solitary waves under intensity-dependent dispersion. IMA Journal of Applied Mathematics.
preprints