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Phase dynamics of periodic wavetrains leading to the 5th order KP equation

Ratliff, Daniel (2017) Phase dynamics of periodic wavetrains leading to the 5th order KP equation Physica D: Nonlinear Phenomena, 353. pp. 11-19.

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Abstract

Using the previous approach outlined in [12, 10], a novel method is presented to derive the fifth order Kadomtsev-Petviashvili (KP) equation from periodic wavetrains. As a result, the coefficients and criterion for the fifth order KP to emerge take a universal form that can be determined a-priori, relating to the system’s conservation laws and the termination of a Jordan chain. Moreover, the analysis reveals that generically a mixed dispersive term qXXXY appears within the final phase equation. The theory presented here is complimented by an example from the context of flexural gravity waves in shallow water and a higher order Nonlinear Schr¨odinger model relevant in plasma physics, demonstrating how the coefficients in this model are determined via elementary calculations.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Ratliff, Danield.ratliff@surrey.ac.ukUNSPECIFIED
Date : 1 September 2017
Identification Number : 10.1016/j.physd.2017.05.004
Copyright Disclaimer : © 2017 Elsevier B.V. All rights reserved.
Uncontrolled Keywords : Lagrangian dynamics; Nonlinear waves; Whitham modulation
Depositing User : Clive Harris
Date Deposited : 30 Aug 2017 07:43
Last Modified : 30 Aug 2017 07:43
URI: http://epubs.surrey.ac.uk/id/eprint/842076

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