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The average solution of a stochastic nonlinear Schrodinger equation under stochastic complex non-homogeneity and complex initial conditions. (English) Zbl 1156.35470

Gavrilova, Marina L. (ed.) et al., Transactions on Computational Science III. Berlin: Springer (ISBN 978-3-642-00211-3/pbk). Lecture Notes in Computer Science 5300. Journal Subline, 143-170 (2009).
Summary: In this paper, a stochastic nonlinear Schrödinger 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.
For the entire collection see [Zbl 1156.68301].

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Software:

Mathematica
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