Phase dynamics of periodic wavetrains leading to the 5th order KP equation
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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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Phase Dynamics of Periodic Wavetrains Leading to the 5th Order KP Equation.pdf - Accepted version Manuscript Download (185kB) | Preview |
Official URL: https://doi.org/10.1016/j.physd.2017.05.004
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 | ||||||
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| Divisions : | Faculty of Engineering and Physical Sciences > Mathematics | ||||||
| Authors : |
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| Date : | 1 September 2017 | ||||||
| DOI : | 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 : | 13 May 2019 02:08 | ||||||
| URI: | http://epubs.surrey.ac.uk/id/eprint/842076 |
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