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• W2079666564 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 newcharacterization 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." @default.
• W2079666564 created "2016-06-24" @default.
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• W2079666564 date "2002-01-01" @default.
• W2079666564 modified "2023-10-13" @default.
• W2079666564 title "Linear Instability of Solitary Wave Solutions of the Kawahara Equation and Its Generalizations" @default.
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• W2079666564 doi "https://doi.org/10.1137/s0036141099361494" @default.
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