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December 2006 On a splitting scheme for the nonlinear Schrödinger equation in a random medium
Renaud Marty
Commun. Math. Sci. 4(4): 679-705 (December 2006).

Abstract

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.

Citation

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Renaud Marty. "On a splitting scheme for the nonlinear Schrödinger equation in a random medium." Commun. Math. Sci. 4 (4) 679 - 705, December 2006.

Information

Published: December 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1121.35131
MathSciNet: MR2264815

Subjects:
Primary: 35Q55
Secondary: 35R60 , 60F05 , 65M70

Keywords: Asymptotic theory , Light waves , Random media , splitting scheme

Rights: Copyright © 2006 International Press of Boston

Vol.4 • No. 4 • December 2006
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