Stability of solitary waves of a generalized two-component Camassa-Holm system

Details Stability of solitary waves of a generalized two-component Camassa-Holm system Stability of solitary waves of a generalized two-component Camassa-Holm system

2010-09-13

arxiv.org/abs/1009.2449v3

Mathematics

Analysis of PDEs

23 pages, 1 figure

Scientific paper

We study here the existence of solitary wave solutions of a generalized two-component Camassa-Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped solitary waves. We also demonstrate that all smooth solitary waves are orbitally stable in the energy space. We finally give a sufficient condition for global strong solutions to the equation without certain parameters.

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