Solitary waves of a coupled Korteweg-de Vries system

Roger Grimshaw and Gerard Iooss

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 62, issue 1, 31-40

Abstract: In the long-wave, weakly nonlinear limit a generic model for the interaction of two waves with nearly coincident linear phase speeds is a pair of coupled Korteweg-de Vries equations. Here we consider the simplest case when the coupling occurs only through linear non-dispersive terms, and for this case delineate the various families of solitary waves that can be expected. Generically, we demonstrate that there will be three families: (a) pure solitary waves which decay to zero at infinity exponentially fast; (b) generalized solitary waves which may tend to small-amplitude oscillations at infinity; and (c) envelope solitary waves which at infinity consist of decaying oscillations. We use a combination of asymptotic methods and the rigorous results obtained from a normal form approach to determine these solitary wave families.

Keywords: Solitary waves; Korteweg-de Vries equations; Normal forms (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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