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arXiv · 1509.08044

Stability of the train of $N$ solitary waves for the two-component Camassa-Holm shallow water system

Xingxing Liu
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Abstract

Considered herein is the integrable two-component Camassa-Holm shallow water system derived in the context of shallow water theory, which admits blow-up solutions and the solitary waves interacting like solitons. Using modulation theory, and combining the almost monotonicity of a local version of energy with the argument on the stability of a single solitary wave, we prove that the train of $N$ solitary waves, which are sufficiently decoupled, is orbitally stable in the energy space $H^1(\R)\times L^2(\R)$.

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Xingxing Liu. 2015-09-27. Stability of the train of $N$ solitary waves for the two-component Camassa-Holm shallow water system. https://arxiv.org/abs/1509.08044

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