Volume 28, Issue 2
The Gaussian Beam Methods for Schrödinger-Poisson Equations

Shi Jin ,  Hao Wu and Xu Yang


J. Comp. Math., 28 (2010), pp. 261-272.

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  • Abstract

As an important model in quantum semiconductor devices, the Schr\"odinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear Schr\"odinger equation, for the Schr\"odinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

  • History

Published online: 2010-04

  • AMS Subject Headings

81Q20, 65M99

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