Multi-symplectic wavelet splitting method for the strongly coupled Schrödinger system

doi:10.1088/1674-1056/21/12/120202

Abstract We propose a multi-symplectic wavelet splitting method to solve the strongly coupled nonlinear Schrödinger equations. Based on its multi-symplectic formulation, the strongly coupled nonlinear Schrödinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, multi-symplectic wavelet collocation method and symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.

Keywords: multi-symplectic wavelet splitting method symplectic Euler method strongly coupled nonlinear Schrödinger equations

Received: 24 May 2012
Revised: 19 June 2012
Published: 01 November 2012

PACS:	02.30.Jr	(Partial differential equations)
	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Jn	(Collocation methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10971226, 91130013, and 11001270), the National Basic Research Program of China (Grant No. 2009CB723802), the Research Innovation Fund of Hunan Province, China (Grant No. CX2011B011), and the Innovation Fund of National University of Defense Technology, China (Grant No. B120205).

Corresponding Authors: Qian Xu
E-mail: qianxu@nudt.edu.cn

Cite this article:

Qian Xu, Chen Ya-Ming, Gao Er, Song Song-He Multi-symplectic wavelet splitting method for the strongly coupled Schrödinger system 2012 Chin. Phys. B 21 120202

[1]	Gross E 1963 J. Math. Phys. 4 195
[2]	Wadati M, Izuka T and Hisakado M 1992 J. Phys. Soc. Jpn. 7 2241
[3]	Aydín A and Karasözen B 2011 J. Comp. Appl. Math. 235 4770
[4]	Cai J 2010 Appl. Math. Comput. 216 2417
[5]	Zhang R, Yu X and Feng T 2012 Chin. Phys. B 21 030202
[6]	Cheng X, Lin J and Wang Z 2007 Acta Phys. Sin. 56 3038 (in Chinese)
[7]	Zhu H, Tang L, Song S, Tang Y and Wang D 2010 J. Comput. Phys. 229 2550
[8]	Zhu H, Song S and Tang Y 2011 Comput. Phys. Commun. 182 616
[9]	Ryland B, McLachlan B and Frank J, 2007 Int. J. Comput. Math. 84 847
[10]	Chen Y, Zhu H and Song S 2010 Comput. Phys. Commun. 181 1231
[11]	Chen Y, Zhu H and Song S 2011 Commun. Theor. Phys. 56 617
[12]	Bridges T J and Reich S 2006 J. Phys. A: Math. Gen. 39 5287
[13]	Hu W and Deng Z 2008 Chin. Phys. B 17 3923
[14]	Bridges T J and Reich S 2001 Phys. Lett. A 284 184
[15]	Reich S 2000 J. Comput. Phys. 157 473
[16]	Bridges T J and Reich S 2001 Physica D 152 491
[17]	Chen J and Qin M 2001 Electron. Trans. Numer. Anal. 12 193
[18]	Moore B and Reich S 2003 Numer. Math. 95 625
[19]	Qian X, Song S, Gao E and Li W 2012 Chin. Phys. B 21 070206
[20]	Chen Y, Song S and Zhu H 2012 Appl. Math. Comput. 218 5552

[1]	The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution Xiang-Wen Cheng(程香雯), Zong-Guo Zhang(张宗国), and Hong-Wei Yang(杨红卫). Chin. Phys. B, 2020, 29(12): 124501.
[2]	Rational solutions and interaction solutions for (2 + 1)-dimensional nonlocal Schrödinger equation Mi Chen(陈觅) and Zhen Wang(王振). Chin. Phys. B, 2020, 29(12): 120201.
[3]	Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws Xian-Guo Geng(耿献国), Fei-Ying Guo(郭飞英), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2020, 29(5): 050201.
[4]	Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation Haifeng Wang(王海峰), Yufeng Zhang(张玉峰). Chin. Phys. B, 2020, 29(4): 040501.
[5]	Lump and interaction solutions to the (3+1)-dimensional Burgers equation Jian Liu(刘健), Jian-Wen Wu(吴剑文). Chin. Phys. B, 2020, 29(3): 030201.
[6]	Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives Hossam A. Ghany, Abd-Allah Hyder, M Zakarya. Chin. Phys. B, 2020, 29(3): 030203.
[7]	Bäcklund transformations, consistent Riccati expansion solvability, and soliton-cnoidal interaction wave solutions of Kadomtsev-Petviashvili equation Ping Liu(刘萍), Jie Cheng(程杰), Bo Ren(任博), Jian-Rong Yang(杨建荣). Chin. Phys. B, 2020, 29(2): 020201.
[8]	Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation Zhao Zhang(张钊), Xiangyu Yang(杨翔宇), Wentao Li(李文涛), Biao Li(李彪). Chin. Phys. B, 2019, 28(11): 110201.
[9]	Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions Xue-Ping Cheng(程雪苹), Wen-Xiu Ma(马文秀), Yun-Qing Yang(杨云青). Chin. Phys. B, 2019, 28(10): 100203.
[10]	Exact solutions of a (2+1)-dimensional extended shallow water wave equation Feng Yuan(袁丰), Jing-Song He(贺劲松), Yi Cheng(程艺). Chin. Phys. B, 2019, 28(10): 100202.
[11]	Painlevé integrability of the supersymmetric Ito equation Feng-Jie Cen(岑锋杰), Yan-Dan Zhao(赵燕丹), Shuang-Yun Fang(房霜韵), Huan Meng(孟欢), Jun Yu(俞军). Chin. Phys. B, 2019, 28(9): 090201.
[12]	A nonlocal Burgers equation in atmospheric dynamical system and its exact solutions Xi-Zhong Liu(刘希忠), Jun Yu(俞军), Zhi-Mei Lou(楼智美), Xian-Min Qian(钱贤民). Chin. Phys. B, 2019, 28(1): 010201.
[13]	N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method Si-Qi Xu(徐思齐), Xian-Guo Geng(耿献国). Chin. Phys. B, 2018, 27(12): 120202.
[14]	A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation Panfeng Zheng(郑攀峰), Man Jia(贾曼). Chin. Phys. B, 2018, 27(12): 120201.
[15]	Truncated series solutions to the (2+1)-dimensional perturbed Boussinesq equation by using the approximate symmetry method Xiao-Yu Jiao(焦小玉). Chin. Phys. B, 2018, 27(10): 100202.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed

Metrics
Related Articles