A diffusion approximation theorem for a nonlinear PDE with application to random birefringent optical fibers

Details A diffusion approximation theorem for a nonlinear PDE with application to random birefringent optical fibers A diffusion approximation theorem for a nonlinear PDE with application to random birefringent optical fibers

2011-05-20

arxiv.org/abs/1105.4048v1

Mathematics

Analysis of PDEs

Scientific paper

In this article, we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schr\"odinger 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-Marty, where a linear electric field is considered, and we get an asymptotic dynamic for the nonlinear electric field.

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