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.

中文翻译：

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关于KdV方程周期多孤子的稳定性

在本文中，我们获得了 KdV 方程的周期性多重孤子的以下稳定性结果： 我们证明在任何给定的小尺寸\(\varepsilon > 0\) 的半线性哈密顿扰动下， KdV 方程，包括大振幅方程，在长度至少为\(O(\varepsilon ^{-2})\)的时间间隔内是轨道稳定的。据我们所知，这是此类可积偏微分方程的大尺寸周期性多孤子的第一个稳定性结果。