Commun. Comput. Phys., 7 (2010), pp. 613-630.


Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrodinger Equation with Trapped Term

Jialin Hong 1*, Linghua Kong 2

1 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China.
2 School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China.

Received 23 March 2009; Accepted (in revised version) 16 June 2009
Available online 9 October 2009
doi:10.4208/cicp.2009.09.057

Abstract

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplectic Fourier spectral (MSFS) methods will be employed to solve the fourth-order Schrodinger equations with trapped term. Using the idea of split-step numerical method and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

AMS subject classifications: 65P10, 65M06, 65M70

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Key words: Schrodinger equation with trapped term, multi-symplectic scheme, Fourier spectral method, conservation law, split-step method.

*Corresponding author.
Email: hjl@lsec.cc.ac.cn (J. Hong), konglh@mail.ustc.edu.cn (L. Kong)
 

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