Dynamics of cubic-quintic nonlinear Schrödinger equation with different parameters

doi:10.1088/1674-1056/25/5/050202

Abstract

We study the dynamics of the cubic-quintic nonlinear Schrödinger equation by the symplectic method. The behaviors of the equation are discussed with harmonically modulated initial conditions, and the contributions from the quintic term are discussed. We observe the elliptic orbit, homoclinic orbit crossing, quasirecurrence, and stochastic motion with different nonlinear parameters in this system. Numerical simulations show that the changing processes of the motion of the system and the trajectories in the phase space are various for different cubic nonlinear parameters with the increase of the quintic nonlinear parameter.

Keywords: nonlinear Schrödinger equation phase space symplectic method

Received: 11 October 2015
Revised: 05 January 2016
Accepted manuscript online:

PACS:	02.60.Cb	(Numerical simulation; solution of equations)
	05.45.Yv	(Solitons)

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11301350, 11472124, and 11271158) and the Doctor Start-up Fund in Liaoning Province, China (Grant No. 20141050).

Corresponding Authors: Wei Hua
E-mail: huawei2030@163.com

Cite this article:

Wei Hua(花巍), Xue-Shen Liu(刘学深), Shi-Xing Liu(刘世兴) Dynamics of cubic-quintic nonlinear Schrödinger equation with different parameters 2016 Chin. Phys. B 25 050202

[1]	He X T and Zhou C T 1993 J. Phys. A: Math. Gen. 26 4123
[2]	Qiao B, Zhou C T, He X T and Lai C H 2008 Commun. Comput. Phys. 4 1129
[3]	Tan Y and Mao J M 2000 J. Phys. A: Math. Gen. 33 9119
[4]	Sheng Q, Khaliq A Q M and Al-Said E A 2001 J. Comput. Phys. 166 400
[5]	Chang Q S, Jia E and Sun W 1999 J. Comput. Phys. 148 397
[6]	Luo X Y, Liu X S and Ding P Z 2007 Acta Phys. Sin. 56 604 (in Chinese)
[7]	Moon H T 1990 Phys. Rev. Lett. 64 412
[8]	Akhmediev N, Eleonskii V M and Kulagin N E 1985 Sov. Phys. JETP 62 894
[9]	Akhmediev N, Eleonskii V M and Kulagin N E 1987 Theor. Math. Phys. 72 809
[10]	Trillio S and Wabnitz S 1991 Opt. Lett. 16 986.
[11]	Feng K 1986 J. Comput. Math. 4 279
[12]	Channell P J and Scovel C 1990 Nonlinearity 3 231
[13]	Reich S 1994 Physica D 76 375
[14]	Gray S K and Manolopoulos D E 1996 J. Chem. Phys. 104 7099
[15]	Bond S D, Leimkuhler B J and Laird B B 1999 J. Comput. Phys. 151 114
[16]	Hua W, Liu X S and Ding P Z 2006 J. Math. Chem. 40 243
[17]	Hua W, Lyu Y and Liu X S 2015 J. Math. Chem. 53 128
[18]	Hua W and Liu S X 2014 Chin. Phys. B 23 020309
[19]	Muruganandam P and Adhikari S K 2003 J. Phys. B: At. Mol. Opt. Phys. 36 2501
[20]	Wang Z X, Zhang X H and Shen K 2008 J. Low. Temp.Phys. 152 136
[21]	Qiu Y F and Wu X 2013 Chin. Phys. Lett. 30 080203
[22]	Zhong S Y, Wu X, Liu S Q and Deng X F 2010 Phys. Rev. D 82 124040
[23]	Zhong S Y and Wu X 2011 Acta. Phys. Sin. 60 090402 (in Chinese)
[24]	Wu X, Huang T Y and Zhang H 2006 Phys. Rev. D 74 083001
[25]	Huang G Q, Ni X T and Wu X 2014 Eur. Phys. J. C 74 3012
[26]	Huang G Q and Wu X 2014 Phys. Rev. D 89 124034
[27]	Wu X and Xie Y 2007 Phys. Rev. D 76 124004
[28]	Wu X and Xie Y 2008 Phys. Rev. D 77 103012
[29]	Sha W, Huang Z X, Chen M S and Wu X L 2008 IEEE Transactions on Antennas and Propagation 56 493
[30]	Shen J, Sha W, Huang Z X, Chen M S and Wu X L 2013 Computer Physics Communications 184 480
[31]	Huang Z X, Xu J, Sun B B, Wu B and Wu X L 2015 Computers and Mathematics with Applications 69 1303
[32]	Jan L C and Anatolij K P 2015 J. Math. Anal. Appl. 430 279
[33]	Liu X S and Ding P Z 2004 J. Phys. A: Math. Gen. 37 1589
[34]	Liu X S, Qi Y Y, He J F and Ding P Z 2007 Commun. Comput. Phys. 2 1
[35]	Sanz-Seran J M 1988 BIT 28 877
[36]	Hong J L and Liu Y 2003 App. Math. Lett. 16 759
[37]	Tang Y F, Vazquez L, Zhang F and Perez-Garcia V M 1996 Computers and Mathematics with Applications 32 73

[1]	Effects of phonon bandgap on phonon-phonon scattering in ultrahigh thermal conductivity θ-phase TaN Chao Wu(吴超), Chenhan Liu(刘晨晗). Chin. Phys. B, 2023, 32(4): 046502.
[2]	Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems Beibei Zhu(朱贝贝), Lun Ji(纪伦), Aiqing Zhu(祝爱卿), and Yifa Tang(唐贻发). Chin. Phys. B, 2023, 32(2): 020204.
[3]	Margolus-Levitin speed limit across quantum to classical regimes based on trace distance Shao-Xiong Wu(武少雄), Chang-Shui Yu(于长水). Chin. Phys. B, 2020, 29(5): 050302.
[4]	Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure Xin-Yun Hu(胡馨匀), Ke-Jian He(何柯健), Zhong-Hua Li(李中华), Guo-Ping Li(李国平). Chin. Phys. B, 2020, 29(5): 050401.
[5]	Study of highly excited vibrational dynamics of HCP integrable system with dynamic potential methods Aixing Wang(王爱星), Lifeng Sun(孙立风), Chao Fang(房超), Yibao Liu(刘义保). Chin. Phys. B, 2020, 29(1): 013101.
[6]	Second order conformal multi-symplectic method for the damped Korteweg-de Vries equation Feng Guo(郭峰). Chin. Phys. B, 2019, 28(5): 050201.
[7]	Dynamics of three nonisospectral nonlinear Schrödinger equations Abdselam Silem, Cheng Zhang(张成), Da-Jun Zhang(张大军). Chin. Phys. B, 2019, 28(2): 020202.
[8]	Exact solitary wave solutions of a nonlinear Schrödinger equation model with saturable-like nonlinearities governing modulated waves in a discrete electrical lattice Serge Bruno Yamgoué, Guy Roger Deffo, Eric Tala-Tebue, François Beceau Pelap. Chin. Phys. B, 2018, 27(12): 126303.
[9]	Nonlinear resonance phenomenon of one-dimensional Bose–Einstein condensate under periodic modulation Hua Wei (花巍), Liu Shi-Xing (刘世兴). Chin. Phys. B, 2014, 23(2): 020309.
[10]	Gradient method for blind chaotic signal separation based on proliferation exponent Lü Shan-Xiang (吕善翔), Wang Zhao-Shan (王兆山), Hu Zhi-Hui (胡志辉), Feng Jiu-Chao (冯久超). Chin. Phys. B, 2014, 23(1): 010506.
[11]	Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients He Jun-Rong (何俊荣), Li Hua-Mei (李画眉). Chin. Phys. B, 2013, 22(4): 040310.
[12]	Multisymplectic implicit and explicit methods for Klein–Gordon–Schrödinger equations Cai Jia-Xiang (蔡加祥), Yang Bin (杨斌), Liang Hua (梁华). Chin. Phys. B, 2013, 22(3): 030209.
[13]	Explicit multi-symplectic method for the Zakharov–Kuznetsov equation Qian Xu(钱旭), Song Song-He(宋松和), Gao Er(高二), and Li Wei-Bin(李伟斌) . Chin. Phys. B, 2012, 21(7): 070206.
[14]	A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation Zhang Rong-Pei(张荣培),Yu Xi-Jun(蔚喜军),and Zhao Guo-Zhong(赵国忠). Chin. Phys. B, 2011, 20(3): 030204.
[15]	The dynamical properties of a Rydberg hydrogen atom between two parallel metal surfaces Liu Wei(刘伟), Li Hong-Yun(李洪云), Yang Shan-Ying(杨善迎), and Lin Sheng-Lu(林圣路). Chin. Phys. B, 2011, 20(3): 033401.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dynamics of cubic-quintic nonlinear Schrödinger equation with different parameters

Cite this article:

Online attention