A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation

doi:10.1088/1674-1056/23/12/120203

Abstract In this paper, we derive a new method for a nonlinear Schrödinger system by using the square of the first-order Fourier spectral differentiation matrix D₁ instead of the traditional second-order Fourier spectral differentiation matrix D₂ to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ‖·‖₂ norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.

Keywords: Fourier pseudospectral method Schrödinger equation conservation law convergence

Received: 21 April 2014
Revised: 18 August 2014
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. 11271195, 41231173, and 11201169), the Postdoctoral Foundation of Jiangsu Province of China (Grant No. 1301030B), the Open Fund Project of Jiangsu Key Laboratory for NSLSCS (Grant No. 201301), and the Fund Project for Highly Educated Talents of Nanjing Forestry University (Grant No. GXL201320).

Corresponding Authors: Lv Zhong-Quan
E-mail: zhqlv@njfu.edu.cn

Cite this article:

Lv Zhong-Quan (吕忠全), Zhang Lu-Ming (张鲁明), Wang Yu-Shun (王雨顺) A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation 2014 Chin. Phys. B 23 120203

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