S. Lafortune and D.E. Pelinovsky
Stability of smooth solitary waves in the b-Camassa-Holm equations
Physica D 440 (2022) 133477 (10 pages)
Abstract:
We derive the precise stability criterion for smooth solitary waves in the
b-family of Camassa-Holm equations. The smooth solitary waves exist on the constant
background. In the integrable cases b = 2 and b = 3, we show analytically that the stability criterion is
satisfied and smooth solitary waves are orbitally stable with respect to
perturbations in H3(R). In the non-integrable cases, we show numerically and asymptotically
that the stability criterion is satisfied for every b > 1. The orbital stability theory
relies on a different Hamiltonian formulation compared to the Hamiltonian formulations
available in the integrable cases.
Keywords:
Camassa-Holm equation; Hamiltonian formulation; smooth solitary waves; orbital stability.