Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

doi:10.1088/1674-1056/24/10/100203

Abstract We propose a new scheme for simulation of a high-order nonlinear Schrödinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respectively. The method is proved to be both charge- and energy-conserved. Various numerical experiments for the equation in different cases are conducted. From the numerical evidence, we see the present method provides an accurate solution and conserves the discrete charge and energy invariants to machine accuracy which are consistent with the theoretical analysis.

Keywords: Schrödinger equation Fourier pseudospectral method conservation law fast Fourier transform

Received: 07 May 2015
Revised: 25 June 2015
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) and the Qing Lan Project of Jiangsu Province, China.

Corresponding Authors: Cai Jia-Xiang
E-mail: thomasjeer@sohu.com

Cite this article:

Cai Jia-Xiang (蔡加祥), Bai Chuan-Zhi (柏传志), Qin Zhi-Lin (秦志林) Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term 2015 Chin. Phys. B 24 100203

[1]	Scott A G, Chu F Y and Mciaughhn D W 1973 Proc. IEEE 61 1443
[2]	Robinson M P 1997 Comput. Math. Appl. 33 39
[3]	Chen J B, Qin M Z and Tang Y F 2002 Comput. Math. Appl. 43 1095
[4]	Hong J L, Liu X and Li C 2007 J. Comput. Phys. 226 1968
[5]	Guan H, Jiao Y, Liu J and Tang Y 2009 Commun. Comput. Phys. 6 639
[6]	Pérez-García V M and Liu X 2003 Appl. Comput. Comput. 144 215
[7]	Wang H 2005 Appl. Math. Comput. 170 17
[8]	Dehghan M and Taleei A 2010 Numer. Meth. Part. D. E. 26 979
[9]	Hong J L and Kong L H 2010 Commun. Comput. Phys. 7 613
[10]	Chao H Y 1987 J. Comput. Math. 5 272
[11]	Zeng W P 1999 J. Comput. Math. 17 133
[12]	Kong L H, Hong J L, Wang L and Fu F F 2009 J. Comput. Appl. Math. 231 664
[13]	Chen J B and Qin M 2001 Electron. Trans. Numer. Anal. 12 193
[14]	Cai J X and Liang H 2012 Chin. Phys. Lett. 29 080201
[15]	Wang J 2009 J. Phys. A: Math. Theor. 42 085205
[16]	Cai J X and Wang Y S 2013 Chin. Phys. B 22 060207
[17]	Lv Z Q, Wang Y S and Song Y Z 2013 Chin. Phys. Lett. 30 030201
[18]	Qian X, Song S H, Gao E and Li W B 2012 Chin. Phys. B 21 070206

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Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

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