Journal
ANNALS OF APPLIED PROBABILITY
Volume 22, Issue 6, Pages 2460-2504Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/11-AAP839
Keywords
Nonlinear Schrodinger equation; stochastic partial differential equations; white noise; diffusion limit
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Funding
- French ANR [ANR-07-44 BLAN-0250]
- Region Ile-de-France
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In this article we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schrodinger equations. This system arises ill the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Gamier and Marty [Wave Motion 43 (2006) 544-560], Marty [Problemes d'evolution en milieux aleatoires: Theoremes limites, schemas numeriques et applications en optique (2005) Univ. Paul Sabatier], where a linear electric field is considered, and we get an asymptotic dynamic for the nonlinear electric field.
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