New Numerical Methods for the Coupled Nonlinear Schrodinger Equations

In this paper, three numerical schemes with high accuracy for the coupled Schrodinger equations are studied. The conserwtive properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split s...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2010-04, Vol.26 (2), p.205-218
Main Authors: Xu, Qiu-bin, Chang, Qian-shun
Format: Article
Language:English
Subjects:
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
孤子碰撞
平面波解
数值方法
无条件稳定
线性分析
非线性薛定谔方程
高精度
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Summary:In this paper, three numerical schemes with high accuracy for the coupled Schrodinger equations are studied. The conserwtive properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-007-7098-2