Stability analysis for nonlinear Schrodinger equations with nonlinear absorbing boundary conditions

Jiwei Zhang, Zhenli Xu, Xiaonan WU, Desheng Wang

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Local absorbing boundary conditions (LABCs) for nonlinear Schrodinger 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.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal of Computational Mathematics
Volume35
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Absorbing boundary conditions
  • Energy estimates
  • Nonlinear Schrodinger equations

Fingerprint

Dive into the research topics of 'Stability analysis for nonlinear Schrodinger equations with nonlinear absorbing boundary conditions'. Together they form a unique fingerprint.

Cite this