On the stability of periodic multi-solitons of the KdV equation. (English) Zbl 1475.35304
Summary: 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.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C08 | Soliton solutions |
| 35B35 | Stability in context of PDEs |
| 35B09 | Positive solutions to PDEs |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
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