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.
Settore MAT/07 - Fisica Matematica
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/859762
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