Artificial boundary conditions for one-dimensional cubic nonlinear Schrodinger equations

被引：74
作者：
Antoine, X
Besse, C
Descombes, S
机构：
[1] Univ Toulouse 3, Lab Math Ind Phys, CNRS, UMR 5640, F-31062 Toulouse 4, France
[2] Ecole Normale Super Lyon, CNRS, UMR 5669, Unite Math Pures & Appl, F-69364 Lyon 07, France
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2006年 / 43卷 / 06期
关键词：
nonlinear cubic Schrodinger equation; artificial boundary conditions; pseudodifferential operators; stable semidiscrete schemes; solitons interaction;
D O I：
10.1137/040606983
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper addresses the construction of nonlinear integro-differential artificial boundary conditions for one-dimensional nonlinear cubic Schrodinger equations. Several ways of designing such conditions are provided and a theoretical classification of their accuracy is given. Semidiscrete time schemes based on the method developed by Duran and Sanz-Serna [IMA J. Numer. Anal. 20 ( 2000), pp. 235 - 261] are derived for these unusual boundary conditions. Stability results are stated and several numerical tests are performed to analyze the capacity of the proposed approach.
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收藏
页码：2272 / 2293
页数：22
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