On the stability of periodic multi-solitons of the KdV equation

TL;DR

This paper proves that a broad class of large-amplitude periodic multi-solitons of the KdV equation remain orbitally stable over long times under small semilinear Hamiltonian perturbations, marking a novel result for large periodic multi-solitons.

Contribution

It establishes the first stability result for large periodic multi-solitons of an integrable PDE under small perturbations, extending stability theory in nonlinear wave equations.

Findings

Large class of multi-solitons are orbitally stable for at least O(ε^{-2}) time.

Stability holds under small semilinear Hamiltonian perturbations.

Includes multi-solitons of large amplitude.

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 $\varepsilon > 0$, 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 $O(\varepsilon^{-2})$. 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.