On the Stability of Periodic Multi-Solitons of the KdV Equation

Abstract

In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size ε>0 , a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least O(ε−2) . To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE.