Stability Analysis for Nonlinear Schrödinger Equations with Nonlinear Absorbing Boundary Conditions

Stability Analysis for Nonlinear Schrödinger Equations with Nonlinear Absorbing Boundary Conditions

Year:    2017

Author:    Jiwei Zhang, Zhenli Xu, Xiaonan Wu, Desheng Wang

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 1–18

Abstract

Local absorbing boundary conditions (LABCs) for nonlinear Schrödinger equations have been constructed in papers [PRE 78(2008) 026709; and PRE 79 (2009) 046711] using the so-called unified approach. In this paper, we present stability analysis for the reduced problem with LABCs on the bounded computational domain by the energy estimate, and discuss a class of modified versions of LABCs. To prove the stability analysis of the reduced problem, we turn to the technique of some auxiliary variables which reduces the higher-order derivatives in LABCs into a family of equations with lower-order derivatives. Furthermore, we extend the strategy to the stability analysis of two-dimensional problems by carefully dealing with the LABCs at corners. Numerical examples are given to demonstrate the effectiveness of our boundary conditions and validate the theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1608-m4507

Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 1–18

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Nonlinear Schrödinger equations Energy estimates Absorbing boundary conditions.

Author Details

Jiwei Zhang

Zhenli Xu

Xiaonan Wu

Desheng Wang