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

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References in corpus (4)

• Rational normal forms and stability of small solutions to nonlinear Schrödinger equations
• Long time dynamics for generalized Korteweg-de Vries and Benjamin-Ono equations
• A non-linear Egorov theorem and Poincaré-Birkhoff normal forms for quasi-linear pdes on the circle
• Normal form coordinates for the KdV equation having expansions in terms of pseudodifferential operators