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

Ratliff, Daniel and Bridges, Tom (2018) Reduction to modified KdV and its KP-like generalization via phase modulation Nonlinearity, 31 (8), 3794.

DJR-TJB_Nonlinearity_April2018.pdf - Accepted version Manuscript

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The main observation of this paper it 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 Schrodinger (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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 9 July 2018
DOI : 10.1088/1361-6544/aabfab
Copyright Disclaimer : Copyright 2018 IOP Publishing
Uncontrolled Keywords : nonlinear waves, Lagrangian fields, phase dynamics
Depositing User : Melanie Hughes
Date Deposited : 20 Apr 2018 14:59
Last Modified : 09 Jul 2019 02:08

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