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

Jiwei Zhang, Zhenli Xu, Xiaonan Wu & Desheng Wang

DOI: 10.4208/jcm.1608-m4507

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 , JiweiXu , ZhenliWu , 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.

Zhang , JiweiXu , ZhenliWu , Xiaonan and Wang , Desheng. (2017). 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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