A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

作者：Qian Xu^*; Song Song-He; Li Wei-Bin

来源：Communications in Theoretical Physics, 2014, 61(6): 703-709.

DOI：10.1088/0253-6102/61/6/08

• conservative algorithm
• coupled nonlinear Schrodinger equation
• multiply components
• unstable wave

Considering the coupled nonlinear Schrodinger 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.

• 出版日期2014-6
• 单位中国人民解放军国防科学技术大学