Conformal structure-preserving method for damped nonlinear Schrödinger equation

doi:10.1088/1674-1056/25/11/110201

Abstract In this paper, we propose a conformal momentum-preserving method to solve a damped nonlinear Schrödinger (DNLS) equation. Based on its damped multi-symplectic formulation, the DNLS system can be split into a Hamiltonian part and a dissipative part. For the Hamiltonian part, the average vector field (AVF) method and implicit midpoint method are employed in spatial and temporal discretizations, respectively. For the dissipative part, we can solve it exactly. The proposed method conserves the conformal momentum conservation law in any local time-space region. With periodic boundary conditions, this method also preserves the total conformal momentum and the dissipation rate of momentum exactly. Numerical experiments are presented to demonstrate the conservative properties of the proposed method.

Keywords: conformal conservation law splitting method conformal momentum-preserving method damped multi-symplectic formulation

Received: 02 May 2016
Revised: 05 July 2016
Accepted manuscript online:

PACS:	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	02.60.-x	(Numerical approximation and analysis)
	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Bf	(Finite-difference methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11571366, 11501570, and 11601514) and the Open Foundation of State Key Laboratory of High Performance Computing of China (Grant No. JC15-02-02).

Corresponding Authors: Hao Fu
E-mail: fuhaosnsn@126.com

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Hao Fu(傅浩), Wei-En Zhou(周炜恩), Xu Qian(钱旭), Song-He Song(宋松和), Li-Ying Zhang(张利英) Conformal structure-preserving method for damped nonlinear Schrödinger equation 2016 Chin. Phys. B 25 110201

[1]	Zhang H, Song S H, Chen X D and Zhou W E 2014 Chin. Phys. B 23070208
[2]	Qian X, Song S H, Gao E and Li W B 2012 Chin. Phys. B 21070206
[3]	Sun J Q, Gu X Y and Ma Z Q 2004 Phys. D 196311328
[4]	Chen Y M, Song S H and Zhu H J 2011 J. Comput. Appl. Math. 2361354
[5]	Cai J X 2010 Appl. Math. Comput. 2162417
[6]	Liao C C, Cui J C, Liang J Z and Ding X H 2016 Chin. Phys. B 25010205
[7]	Cai J X, Wang J L and Wang Y S 2015 Chin. Phys. B 24050205
[8]	Cai W J, Wang Y S and Song Y Z 2014 Chin. Phys. Lett. 31040201
[9]	Chen J B, Qin M Z and Tang Y F 2002 Comput. Math. Appl. 431095
[10]	Fu F F, Kong L H and Wang L 2009 Adv. Appl. Math. Mech. 1699
[11]	Islas A L, Karpeev D A and Schober C M 2001 J. Comput. Phys. 173116
[12]	Moore B E and Reich S 2003 Future Gener. Comput. Syst. 19395
[13]	Bridges T J and Reich S 2001 Phys. Lett. A 284184
[14]	Bridges T J and Reich S 2001 Phys. D 152491
[15]	Chen J B and Qin M Z 2001 Electron. Trans. Numer. Anal. 12193
[16]	Hong J L, Liu X Y and Li C 2007 J. Comput. Phys. 2261968
[17]	Gong Y Z, Cai J X and Wang Y S 2014 J. Comput. Phys. 27980
[18]	Elphick C and Meron E 1989 Phys. Rev. A 403226
[19]	Deutsch I H and Abram I 1994 J. Opt. Soc. Am. B 112303
[20]	Perlmutter M and McLachlan R 2001 J. Geom. Phys. 39276
[21]	McLachlan R I and Quispel G R W 2002 Acta Numer. 11699
[22]	Moore B E 2009 Math. Comput. Simulat. 8020
[23]	Moore B E, Noreña L and Schober C M 2013 J. Comput. Phys. 23280

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