Communications in Mathematical Sciences

On a splitting scheme for the nonlinear Schrödinger equation in a random medium

Renaud Marty

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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.

Article information

Source
Commun. Math. Sci., Volume 4, Number 4 (2006), 679-705.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.cms/1175797606

Mathematical Reviews number (MathSciNet)
MR2264815

Zentralblatt MATH identifier
1121.35131

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60F05: Central limit and other weak theorems 65M70: Spectral, collocation and related methods

Keywords
Light waves random media asymptotic theory splitting scheme

Citation

Marty, Renaud. On a splitting scheme for the nonlinear Schrödinger equation in a random medium. Commun. Math. Sci. 4 (2006), no. 4, 679--705. https://projecteuclid.org/euclid.cms/1175797606


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