id: 06130624
dt: j
an: 
au: de Bouard, A.; Gazeau, M.
ti: A diffusion approximation theorem for a nonlinear PDE with application to
    random birefringent optical fibers.
so: Ann. Appl. Probab. 22, No. 6, 2460-2504 (2012).
py: 2012
pu: Institute of Mathematical Statistics, Hayward, CA
la: EN
cc: 35Q55 60H15
ut: nonlinear Schrödinger equation; stochastic partial differential equations;
    white noise; diffusion limit
ci: 
li: euclid:aoap/1353695959 doi:10.1214/11-AAP839
ab: Summary: In this article we propose a generalization of the theory of
    diffusion approximation for random ODE to a nonlinear system of random
    Schrödinger equations. This system arises in 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 Garnier and Marty [Wave Motion
    43 (2006) 544-560], Marty [Problèmes d’évolution en milieux
    aléatoires: Théorèmes limites, schémas numériques 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.
rv: