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Phase dynamics of periodic waves leading to the Kadomtsev-Petviashvili equation in 3+1 dimensions

Bridges, TJ and Ratliff, DJ (2015) Phase dynamics of periodic waves leading to the Kadomtsev-Petviashvili equation in 3+1 dimensions Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences, 471 (2178).

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Abstract

The Kadomstev-Petviashvili (KP) equation is a well-known modulation equation normally derived by starting with the trivial state and an appropriate dispersion relation. In this paper it is shown that the KP equation is also the relevant modulation equation for bifurcation from periodic travelling waves when the wave action flux has a critical point. Moreover, the emergent KP equation arises in a universal form, with the coefficients determined by the components of the conservatio n of wave action. The theory is derived for a general class of partial differential equations generated by a Lagrangian using phase modulation. The theory extends to any space dimension and time, but the emphasis in the paper is on the ca se of 3+1. Motivated by light bullets and quantum vortex dynamics, the theory is illustrated by showing how defocussing NLS in 3+1 bifurcates to KP in 3+1 at criticality. The generalization to $N>3$ is also discussed.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Bridges, TJUNSPECIFIEDUNSPECIFIED
Ratliff, DJUNSPECIFIEDUNSPECIFIED
Date : 27 May 2015
Identification Number : 10.1098/rspa.2015.0137
Uncontrolled Keywords : nonlinear waves, Lagrangian systems, travelling waves, wave action, modulation
Additional Information : © 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License
Depositing User : Symplectic Elements
Date Deposited : 19 Jun 2015 09:06
Last Modified : 29 Jun 2015 13:33
URI: http://epubs.surrey.ac.uk/id/eprint/807797

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