The modulation of multiple phases leading to the modified Korteweg–de Vries equation

Ratliff, Daniel (2018) The modulation of multiple phases leading to the modified Korteweg–de Vries equation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28 (9). 093117. ISSN 1054-1500

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Official URL: https://doi.org/10.1063/1.5037280

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.

Item Type: Article
Uncontrolled Keywords: Modulation, Lagrangian Dynamics, Nonlinear Waves
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 14 Aug 2020 13:32
Last Modified: 14 Aug 2020 13:45
URI: http://nrl.northumbria.ac.uk/id/eprint/44091

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