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 ε> 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(ε- 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.
On the Stability of Periodic Multi-Solitons of the KdV Equation / T. Kappeler, R. Montalto. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 385:3(2021), pp. 1871-1956. [10.1007/s00220-021-04089-9]
On the Stability of Periodic Multi-Solitons of the KdV Equation
R. Montalto
2021
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 ε> 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(ε- 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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