Reduction to modified KdV and its KP-like generalization via phase modulation

Daniel J. Ratliff, Thomas J. Bridges

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
1 Downloads (Pure)

Abstract

The main observation of this paper is that the modified Korteweg-de Vries equation has its natural origin in phase modulation of a basic state such as a periodic travelling wave, or more generally, a family of relative equilibria. Extension to 2 + 1 suggests that a modified Kadomtsev-Petviashvili (or a Konopelchenko-Dubrovsky) equation should emerge, but our result shows that there is an additional term which has gone heretofore unnoticed. Thus, through the novel application of phase modulation a new equation appears as the 2 + 1 extension to a previously known one. To demonstrate the theory it is applied to the cubic-quintic nonlinear Schrödinger (CQNLS) equation, showing that there are relevant parameter values where a modified KP equation bifurcates from periodic travelling wave solutions of the 2 + 1 CQNLS equation.

Original languageEnglish
Pages (from-to)3794-3813
Number of pages20
JournalNonlinearity
Volume31
Issue number8
DOIs
Publication statusPublished - 9 Jul 2018
Externally publishedYes

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