Parameter Extension and the Quasi-Rational Solution of a Lattice Boussinesq Equation

doi:10.1088/0256-307X/30/4/040201

Chin. Phys. Lett.

2013, Vol. 30

Issue (4): 040201 DOI: 10.1088/0256-307X/30/4/040201

GENERAL

Parameter Extension and the Quasi-Rational Solution of a Lattice Boussinesq Equation

NONG Li-Juan^**, ZHANG Da-Jun, SHI Ying, ZHANG Wen-Ying

Department of Mathematics, Shanghai University, Shanghai 200444

Cite this article:

NONG Li-Juan, ZHANG Da-Jun, SHI Ying et al 2013 Chin. Phys. Lett. 30 040201

Download: PDF(420KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract For a lattice Boussinesq equation, we introduce a simple-parameter invertible transformation by which the equation is transformed into an extended version. This new equation admits solitons and nonzero quasi-rational solutions, both in Casoratian form. These solutions can be reverted to those of the lattice Boussinesq equation.

Received: 13 January 2013 Published: 28 April 2013

PACS:	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/30/4/040201 OR https://cpl.iphy.ac.cn/Y2013/V30/I4/040201

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	NONG Li-Juan
	ZHANG Da-Jun
	SHI Ying
	ZHANG Wen-Ying

[1] Nijhoff F W et al 1983 Phys. Lett. A 97 125
[2] Adler V E et al 2003 Commun. Math. Phys. 233 513
[3] Nijhoff F W and Walker A J 2001 Glasgow Math. J. 43A 109
[4] Bobenko A I and Suris Y B 2002 Int. Math. Res. Not. 2002 573
[5] Hietarinta J 2011 J. Phys. A: Math. Theor. 44 165204
[6] Zhang D J et al 2012 Stud. Appl. Math. 129 220
[7] Walker A J 2001 PhD Dissertation (Leeds: University of Leeds)
[8] Tongas A and Nijhoff F W 2005 Glasgow Math. J. 47A 205
[9] Hietarinta J and Zhang D J 2010 J. Math. Phys. 51 033505
[10] Hietarinta J and Zhang D J 2011 SIGMA 7 061
[11] Nijhoff F W et al 2009 J. Phys. A: Math. Theor. 42 404005
[12] Zhang D J and Zhao S L 2012 arXiv:1208.3752[nlin.SI]
[13] Hietarinta J and Zhang D J 2009 J. Phys. A: Math. Theor. 42 404006
[14] Atkinson J and Nijhoff F 2010 Commun. Math. Phys. 299 283
[15] Nijhoff F W and Atkinson J 2010 Int. Math. Res. Not. 2010 3837
[16] Butler S and Joshi N 2010 Inverse Probl. 26 115012
[17] Cao C W and Xu X X 2012 J. Phys. A: Math. Theor. 45 055213
[18] Cao C W and Zhang G Y 2012 J. Phys. A: Math. Theor. 45 095203
[19] Zhang D J 2006 arXiv:nlin/0603008v3[nlin.SI]
[20] Wu H and Zhang D J 2003 J. Phys. A: Math. Gen. 36 4867
[21] Zhang D J and Hietarinta J 2010 AIP Conf. Proc. Ed. Ma W X, Hu X B and Liu Q P 1212 154
[22] Shi Y and Zhang D J 2011 SIGMA 7 046
[23] Sun Y Y and Zhang D J 2012 Commun. Theor. Phys. 57 923
[24] Freeman N C and Nimmo J J C 1983 Phys. Lett. A 95 1

Related articles from Frontiers Journals

[1]	S. Y. Lou, Man Jia, and Xia-Zhi Hao. Higher Dimensional Camassa–Holm Equations[J]. Chin. Phys. Lett., 2023, 40(2): 040201
[2]	Wen-Xiu Ma. Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions[J]. Chin. Phys. Lett., 2022, 39(10): 040201
[3]	Chong Liu, Shao-Chun Chen, Xiankun Yao, and Nail Akhmediev. Modulation Instability and Non-Degenerate Akhmediev Breathers of Manakov Equations[J]. Chin. Phys. Lett., 2022, 39(9): 040201
[4]	Xiao-Man Zhang, Yan-Hong Qin, Li-Ming Ling, and Li-Chen Zhao. Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation[J]. Chin. Phys. Lett., 2021, 38(9): 040201
[5]	Kai-Hua Yin, Xue-Ping Cheng, and Ji Lin. Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation[J]. Chin. Phys. Lett., 2021, 38(8): 040201
[6]	Yusong Cao and Junpeng Cao. Exact Solution of a Non-Hermitian Generalized Rabi Model[J]. Chin. Phys. Lett., 2021, 38(8): 040201
[7]	Zequn Qi , Zhao Zhang , and Biao Li. Space-Curved Resonant Line Solitons in a Generalized $(2+1)$-Dimensional Fifth-Order KdV System[J]. Chin. Phys. Lett., 2021, 38(6): 040201
[8]	Wei Wang, Ruoxia Yao, and Senyue Lou. Abundant Traveling Wave Structures of (1+1)-Dimensional Sawada–Kotera Equation: Few Cycle Solitons and Soliton Molecules[J]. Chin. Phys. Lett., 2020, 37(10): 040201
[9]	Li-Chen Zhao, Yan-Hong Qin, Wen-Long Wang, Zhan-Ying Yang. A Direct Derivation of the Dark Soliton Excitation Energy[J]. Chin. Phys. Lett., 2020, 37(5): 040201
[10]	Danda Zhang, Da-Jun Zhang, Sen-Yue Lou. Lax Pairs of Integrable Systems in Bidifferential Graded Algebras[J]. Chin. Phys. Lett., 2020, 37(4): 040201
[11]	Yu-Han Wu, Chong Liu, Zhan-Ying Yang, Wen-Li Yang. Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction[J]. Chin. Phys. Lett., 2020, 37(4): 040201
[12]	Bao Wang, Zhao Zhang, Biao Li. Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schr?dinger Equation[J]. Chin. Phys. Lett., 2020, 37(3): 040201
[13]	Zhao Zhang, Shu-Xin Yang, Biao Li. Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation[J]. Chin. Phys. Lett., 2019, 36(12): 040201
[14]	Zhou-Zheng Kang, Tie-Cheng Xia. Construction of Multi-soliton Solutions of the $N$-Coupled Hirota Equations in an Optical Fiber[J]. Chin. Phys. Lett., 2019, 36(11): 040201
[15]	Yong-Shuai Zhang, Jing-Song He. Bound-State Soliton Solutions of the Nonlinear Schr?dinger Equation and Their Asymmetric Decompositions[J]. Chin. Phys. Lett., 2019, 36(3): 040201

Viewed

Full text

Abstract