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

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 $H^1(\mathbb{R})\times L^2(\mathbb{R})$.

References in corpus (5)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• On an integrable two-component Camassa-Holm shallow water system
• Two component integrable systems modelling shallow water waves: the constant vorticity case
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Cited by in corpus (1)

• Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy