@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 = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1608-m4507},
url = {http://global-sci.org/intro/article_detail/jcm/9760.html}
}