Volume 35, Issue 1
Stability Analysis for Nonlinear Schrödinger Equations with Nonlinear Absorbing Boundary Conditions

Jiwei Zhang, Zhenli Xu, Xiaonan WuDesheng Wang

J. Comp. Math., 35 (2017), pp. 1-18.

Published online: 2017-02

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  • 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.

  • Keywords

Nonlinear Schrödinger equations, Energy estimates, Absorbing boundary conditions.

  • AMS Subject Headings

65M12, 65M06, 65M15.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jwzhang@csrc.ac.cn (Jiwei Zhang)

xuzl@sjtu.edu.cn (Zhenli Xu)

xwu@hkbu.edu.hk (Xiaonan Wu)

desheng@ntu.edu.sg (Desheng Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-35-1, author = {Zhang , Jiwei and Xu , Zhenli and Wu , Xiaonan and Wang , Desheng}, title = {Stability Analysis for Nonlinear Schrödinger Equations with Nonlinear Absorbing Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {1}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1608-m4507}, url = {http://global-sci.org/intro/article_detail/jcm/9760.html} }
TY - JOUR T1 - Stability Analysis for Nonlinear Schrödinger Equations with Nonlinear Absorbing Boundary Conditions AU - Zhang , Jiwei AU - Xu , Zhenli AU - Wu , Xiaonan AU - Wang , Desheng JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 18 PY - 2017 DA - 2017/02 SN - 35 DO - http://doi.org/10.4208/jcm.1608-m4507 UR - https://global-sci.org/intro/article_detail/jcm/9760.html KW - Nonlinear Schrödinger equations, Energy estimates, Absorbing boundary conditions. AB -

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.

Jiwei Zhang, Zhenli Xu, Xiaonan Wu & Desheng Wang. (2020). Stability Analysis for Nonlinear Schrödinger Equations with Nonlinear Absorbing Boundary Conditions. Journal of Computational Mathematics. 35 (1). 1-18. doi:10.4208/jcm.1608-m4507
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