A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components |
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引用本文: | 钱旭,宋松和,李伟斌.A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components[J].理论物理通讯,2014(6). |
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作者姓名: | 钱旭 宋松和 李伟斌 |
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基金项目: | Supported by the National Natural Science Foundation of China under Grant No.91130013;Hunan Provincial Innovation Foundation under Grant No.CX2012B010;the Innovation Fund of National University of Defense Technology under Grant No.B120205;the Open Foundation of State Key Laboratory |
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摘 要: | Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
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关 键 词: | conservative algorithm coupled nonlinear Schr¨odinger equation multiply components unstable wave |
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