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Universal Geometric Condition for the Transverse Instability of Solitary Waves

Bridges, Thomas J. (2000) Universal Geometric Condition for the Transverse Instability of Solitary Waves Physical Review Letters, 84. pp. 2614-2617.

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Abstract

Transverse instabilities correspond to a class of perturbations traveling in a direction transverse to the direction of the basic solitary wave. Solitary waves traveling in one space direction generally come in one-parameter families. We embed them in a two-parameter family and deduce a new geometric condition for transverse instability of solitary waves. This condition is universal in the sense that it does not require explicit properties of the solitary wave—or the governing equation. In this paper the basic idea is presented and applied to the Zakharov-Kuznetsov equation for illustration. An indication of how the theory applies to a large class of equations in physics and oceanography is also discussed.

Item Type: Article
Additional Information: Published i Physical Review Letters, 84, 2614-2617. © 2000 The American Physical Society.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1459

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