Communications in Mathematical Sciences

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

Renaud Marty

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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

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

First available in Project Euclid: 5 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Light waves random media asymptotic theory splitting scheme


Marty, Renaud. On a splitting scheme for the nonlinear Schrödinger equation in a random medium. Commun. Math. Sci. 4 (2006), no. 4, 679--705.

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