STABILITY OF SOLITONS UNDER RAPIDLY OSCILLATING RANDOM PERTURBATIONS OF THE INITIAL CONDITIONS
成果类型：
Article
署名作者：
Fedrizzi, Ennio
署名单位：
Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/13-AAP931
发表日期：
2014
页码：
616-651
关键词：
摘要：
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 Schrodinger 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.