Stability of n-solitons for the Camassa-Holm equation

Abstract

In this paper, we investigate the stability of n-soliton solutions to the Camassa-Holm (CH) equation. This is achieved by constructing a Lyapunov functional comprised of local independent conservation laws and higher order terms. We first address the issue of non-uniqueness of local conservation laws arising from the recursion operator, and establish the linear representation between two series of local laws generated by the bi-Hamiltonian structure. With the construction of local independent laws, it is then demonstrated that n-solitons actually realize non-isolated constraint minimizers, based on spectral analysis and computation of Wronskain determinant.