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Chin. Phys. B, 2013, Vol. 22(6): 060207    DOI: 10.1088/1674-1056/22/6/060207
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A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system

Cai Jia-Xianga b, Wang Yu-Shuna
a Jiangsu Key Laboratory for NSLSCS, School of Mathematics Science, Nanjing Normal University, Nanjing 210046, China;
b School of Mathematics Science, Huaiyin Normal University, Huaian 223300, China
Abstract  We derive a new method for coupled nonlinear Schrödinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of solitons collision. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.
Keywords:  Schrödinger equation      Fourier pseudospectral method      conservation law      energy  
Received:  09 October 2012      Revised:  06 December 2012      Accepted manuscript online: 
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.70.Bf (Finite-difference methods)  
  02.70.Jn (Collocation methods)  
  02.70.Hm (Spectral methods)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11201169 and 11271195), the National Basic Research Program of China (Grant No. 2010AA012304), the Natural Science Foundation of Jiangsu Education Bureau, China (Grant Nos. 10KJB110001 and 12KJB110002), and the Qing Lan Project of Jiangsu Province of China.
Corresponding Authors:  Wang Yu-Shun     E-mail:  thomasjeer@sohu.com, wangyushun@njnu.edu.cn

Cite this article: 

Cai Jia-Xiang, Wang Yu-Shun A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system 2013 Chin. Phys. B 22 060207

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