Strong order of convergence of a semidiscrete scheme for the stochastic Manakov equation

It is well accepted by physicists that the Manakov PMD equation is a good model to describe the evolution of nonlinear electric fields in optical fibers with randomly varying birefringence. In the regime of the diffusion approximation theory, an effective asymptotic dynamics has recently been obtained to describe this evolution. This equation is called the stochastic Manakov equation. In this article, we propose a semidiscrete version of a Crank Nicolson scheme for this limit equation and we analyze the strong error. Allowing sufficient regularity of the initial data, we prove that the numerical scheme has strong order 1/2