Linear Instability of Solitary Wave Solutions of the Kawahara Equation and Its Generalizations
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Bridges, Thomas 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 |
| ID Code: | 1403 |
| Deposited By: | Mr Adam Field |
| Deposited On: | 27 May 2010 15:40 |
| Last Modified: | 28 Sep 2012 10:50 |
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