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.
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.
|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|
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