Exact Elliptic Compactons in Generalized Korteweg-DeVries Equations

Details Exact Elliptic Compactons in Generalized Korteweg-DeVries Equations Exact Elliptic Compactons in Generalized Korteweg-DeVries Equations

2005-08-04

arxiv.org/abs/nlin/0508010v1

Nonlinear Sciences

Pattern Formation and Solitons

Four pages, no figures

Scientific paper

We derive a general theorem relating the energy, momentum and velocity of any solitary wave solution of the generalized KdV equation which enables us to relate the amplitude, width, and momentum to the velocity of these solutions. We obtain the general condition for linear and Lyapunov stability. We then obtain a two parameter family of exact solutions to these equations which include elliptic and hyper-elliptic compacton solutions. For this general family we explicitly verify both the theorem and the stability criteria.

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