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arXiv · 2009.02721

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

Thomas Kappeler·Riccardo Montalto
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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.

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Thomas Kappeler, Riccardo Montalto. 2020-09-06. On the stability of periodic multi-solitons of the KdV equation. https://doi.org/10.1007/s00220-021-04089-9

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