The Average Solution of a Stochastic Nonlinear Schrodinger Equation under Stochastic Complex Non-homogeneity and Complex Initial Conditions

Abstract

In this paper, a stochastic nonlinear Schrodinger equation is studied under stochastic complex non-homogeneity in a limited time interval through homogeneous boundary conditions and complex initial conditions. The analytical solution for the linear case is introduced. The Wiener-Hermite expansion together with the perturbation method, the WHEP technique, is used to get approximate ensemble average of the stochastic solution process. Using Mathematica, the solution algorithm is tested through computing the first order approximation of the solution ensemble average. The method is illustrated through case studies which demonstrate the effects of the initial conditions as well as the input non-homogeneities.KeywordsStochastic Nonlinear Schrodinger EquationPerturbationEigenfunction ExpansionWHEP TechniqueWiener-Hermite Expansion