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Linear Instability of Solitary Wave Solutions of the Kawahara Equation and Its Generalizations

Bridges, T.J. and Derks, Gianne (2002) Linear Instability of Solitary Wave Solutions of the Kawahara Equation and Its Generalizations the <i>SIAM Journal on Mathematical Analysis</i>, 33. pp. 1356-1378.

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Abstract

The linear stability problem for solitary wave states of the Kawahara---or fifth-order KdV-type---equation and its generalizations is considered. A new formulation of the stability problem in terms of the symplectic Evans matrix is presented. The formulation is based on a multisymplectification of the Kawahara equation, and leads to a new characterization of the basic solitary wave, including changes in the state at infinity represented by embedding the solitary wave in a multiparameter family. The theory is used to give a rigorous geometric sufficient condition for instability. The theory is abstract and applies to a wide range of solitary wave states. For example, the theory is applied to the families of solitary waves found by Kichenassamy--Olver and Levandosky.

Item Type: Article
Additional Information: Published in the SIAM Journal on Mathematical Analysis, Volume 33, Number 6, pp. 1356-1378. © 2002 Society for Industrial and Applied Mathematics
Uncontrolled Keywords: solitary waves, Evans function, multisymplectic structures
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 08 Nov 2013 10:16
URI: http://epubs.surrey.ac.uk/id/eprint/1403

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