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arXiv · 2210.00172

Orbital stability of smooth solitary waves for the $b$-family of Camassa-Holm equations

Teng Long·Changjian Liu
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Abstract

In this paper, we study the stability of smooth solitary waves for the $b$-family of Camassa-Holm equations. We verify the stability criterion analytically for the general case $b>1$ by the idea of the monotonicity of the period function for planar Hamiltonian systems and show that the smooth solitary waves are orbitally stable, which gives a positive answer to the open problem proposed by Lafortune and Pelinovsky [S. Lafortune, D. E. Pelinovsky, Stability of smooth solitary waves in the $b$-Camassa-Holm equation].

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Teng Long, Changjian Liu. 2022-10-01. Orbital stability of smooth solitary waves for the $b$-family of Camassa-Holm equations. https://doi.org/10.1016/j.physd.2023.133680

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