Dmitry E Pelinovsky - McMaster Experts

Affiliations

Faculty of Science, McMaster University
Mathematics and Statistics (Internal), Faculty of Science
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

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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
- Peaked Stokes waves as solutions of Babenko's equation. Applied Mathematics Letters. 161:109359. 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
- 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. 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
- Bifurcations of Asymmetric Vortices in Symmetric Harmonic Traps. Applied Mathematics Research eXpress. 2013:127-164. 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
- 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
preprints