Stability of solitons under rapidly oscillating random perturbations of the initial conditions

Abstract : We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of the initial conditions: for a wide class of rapidly oscillating random perturbations this problem reduces to the study of a canonical system of stochastic differential equations which depends only on the integrated covariance of the perturbation. We finally study the problem when the perturbation is weak, which allows us to analyze the stability of solitons quantitatively.
Type de document :
Pré-publication, Document de travail
Published in at http://dx.doi.org/10.1214/13-AAP931 the Annals of Applied Probability (http://www.. 2011
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https://hal.archives-ouvertes.fr/hal-01017943
Contributeur : Ennio Fedrizzi <>
Soumis le : jeudi 3 juillet 2014 - 14:17:45
Dernière modification le : lundi 29 mai 2017 - 14:24:29

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  • HAL Id : hal-01017943, version 1
  • ARXIV : 1201.3753

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Ennio Fedrizzi. Stability of solitons under rapidly oscillating random perturbations of the initial conditions. Published in at http://dx.doi.org/10.1214/13-AAP931 the Annals of Applied Probability (http://www.. 2011. 〈hal-01017943〉

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