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 - <p style="text-align: justify;">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.</p>