The Modulation of Multiple Phases Leading to the Modified Korteweg-de Vries Equation

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Abstract

This paper seeks to derive the modified KdV (mKdV) equation using a novel approach from systems generated from abstract Lagrangians that possess a two-parameter symmetry group. The method to do uses a modified modulation approach, which results in the mKdV emerging with coefficients related to the conservation laws possessed by the original Lagrangian system. Alongside this, an adaptation of the method of Kuramoto is developed, providing a simpler mechanism to determine the coefficients of the nonlinear term. The theory is illustrated using two examples of physical interest, one in stratified hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to illustrate how the criterion for the mKdV equation to emerge may be assessed and its coefficients generated.
Original languageEnglish
Article number093117
Number of pages15
JournalChaos
Volume28
Issue number9
DOIs
Publication statusPublished - 27 Sep 2018
Externally publishedYes

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