Abstract
This paper is devoted to 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 (2022).
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