Journal article
Periodic Waves in the Fractional Modified Korteweg–de Vries Equation
Abstract
Periodic waves in the modified Korteweg–de Vries (mKdV) equation are revisited in the setting of the fractional Laplacian. Two families of solutions in the local case are given by the sign-definite dnoidal and sign-indefinite cnoidal solutions. Both solutions can be characterized in the general fractional case as global minimizers of the quadratic part of the energy functional subject to the fixed L4$$L^4$$ norm: the sign-definite …
Authors
Natali F; Le U; Pelinovsky DE
Journal
Journal of Dynamics and Differential Equations, Vol. 34, No. 2, pp. 1601–1640
Publisher
Springer Nature
Publication Date
June 2022
DOI
10.1007/s10884-021-10000-w
ISSN
1040-7294