Communications in Mathematical Sciences
Volume 4 (2006)
On a splitting scheme for the nonlinear Schrödinger equation in a random medium
Pages: 679 – 705
In this paper we consider a nonlinear Schrödinger equation (NLS) with random coefficients, in a regime of separation of scales corresponding to diffusion approximation. The primary goal of this paper is to propose and study an efficient numerical scheme in this framework. We use a pseudo-spectral splitting scheme and we establish the order of the global error. In particular we show that we can take an integration step larger than the smallest scale of the problem, here the correlation length of the random medium. We study the asymptotic behavior of the numerical solution in the diffusion approximation regime.
Light waves; random media; asymptotic theory; splitting scheme
2010 Mathematics Subject Classification
Primary 35Q55. Secondary 35R60, 60F05, 65M70.