Chin. Phys. Lett.  2012, Vol. 29 Issue (6): 060203    DOI: 10.1088/0256-307X/29/6/060203
GENERAL |
Exact Solutions to a Toda-Like Lattice Equation in 2+1 Dimensions
WU Yong-Qi**
1Mathematics and Computational Science School, Zhanjiang Normal University, Zhanjiang 524048
Cite this article:   
WU Yong-Qi 2012 Chin. Phys. Lett. 29 060203
Download: PDF(425KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

A completely integrable Toda-like lattice equation in 2+1 dimensions is studied. Four kinds of exact solutions to this equation are derived by virtue of variable separation and the Hirota bilinear approach. The relations between each two solutions are also presented.

Received: 13 February 2012      Published: 31 May 2012
PACS:  02.30.Jr (Partial differential equations)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/29/6/060203       OR      https://cpl.iphy.ac.cn/Y2012/V29/I6/060203
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
WU Yong-Qi

[1] Cao C W, Geng X G and Wu Y T 1999 J. Phys. A: Math. Gen. 32 8059

[2] Tam H W, Hu X B and Qian X M 2002 J. Math. Phys. 43 1008

[3] Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)

[4] Matsuno Y 1984 Bilinear Transformation Method (London: Academic Press Inc.)

[5] Farkas H M and Kra I 1992 Riemann Surfaces (New York: Springer-Verlag)

[6] Nakamura A 1979 J. Phys. Soc. Jpn. 47 1701

[7] Hu X B, Clarkson P A and Bullough R 1997 J. Phys. A: Math. Gen. 30 L669

[8] Hon Y C, Fan E G and Qin Z Y 2008 Mod. Phys. Lett. B 22 547

[9] Fan E G and Hon Y C 2008 Phys. Rev. E 78 036607

[10] Ma W X, Zhou R G and Gao L 2009 Mod. Phys. Lett. A 24 1677

[11] Cai K J, Tian B, Zhang H and Meng X H 2009 Commun. Theor. Phys. 52 473

[12] Wu Y Q 2010 Appl. Math. Comput. 216 3154

[13] Wu Y Q 2008 Chin. Phys. Lett. 25 2739

[14] Wu Y Q 2011 Chin. Phys. Lett. 28 060204

Related articles from Frontiers Journals
[1] 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): 060203
[2] Danda Zhang, Da-Jun Zhang, Sen-Yue Lou. Lax Pairs of Integrable Systems in Bidifferential Graded Algebras[J]. Chin. Phys. Lett., 2020, 37(4): 060203
[3] 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): 060203
[4] Zhou-Zheng Kang, Tie-Cheng Xia, Xi Ma. Multi-Soliton Solutions for the Coupled Fokas–Lenells System via Riemann–Hilbert Approach[J]. Chin. Phys. Lett., 2018, 35(7): 060203
[5] Zhao-Wen Yan, Mei-Na Zhang Ji-Feng Cui. Higher-Order Inhomogeneous Generalized Heisenberg Supermagnetic Model[J]. Chin. Phys. Lett., 2018, 35(5): 060203
[6] Yu Wang, Biao Li, Hong-Li An. Dark Sharma–Tasso–Olver Equations and Their Recursion Operators[J]. Chin. Phys. Lett., 2018, 35(1): 060203
[7] Zhong Han, Yong Chen. Bright-Dark Mixed $N$-Soliton Solution of the Two-Dimensional Maccari System[J]. Chin. Phys. Lett., 2017, 34(7): 060203
[8] Zhao-Wen Yan, Xiao-Li Wang, Min-Li Li. Fermionic Covariant Prolongation Structure for a Super Nonlinear Evolution Equation in 2+1 Dimensions[J]. Chin. Phys. Lett., 2017, 34(7): 060203
[9] Sen-Yue Lou. From Nothing to Something II: Nonlinear Systems via Consistent Correlated Bang[J]. Chin. Phys. Lett., 2017, 34(6): 060203
[10] Yun-Kai Liu, Biao Li. Rogue Waves in the (2+1)-Dimensional Nonlinear Schr?dinger Equation with a Parity-Time-Symmetric Potential[J]. Chin. Phys. Lett., 2017, 34(1): 060203
[11] Chao Qian, Ji-Guang Rao, Yao-Bin Liu, Jing-Song He. Rogue Waves in the Three-Dimensional Kadomtsev–Petviashvili Equation[J]. Chin. Phys. Lett., 2016, 33(11): 060203
[12] Ming-Zhan Song, Xu Qian, Song-He Song. Modified Structure-Preserving Schemes for the Degasperis–Procesi Equation[J]. Chin. Phys. Lett., 2016, 33(11): 060203
[13] HU Xiao-Rui, CHEN Jun-Chao, CHEN Yong. Groups Analysis and Localized Solutions of the (2+1)-Dimensional Ito Equation[J]. Chin. Phys. Lett., 2015, 32(07): 060203
[14] CHEN Hai, ZHOU Zi-Xiang. Darboux Transformation with a Double Spectral Parameter for the Myrzakulov-I Equation[J]. Chin. Phys. Lett., 2014, 31(12): 060203
[15] CHEN Jun-Chao, CHEN Yong, FENG Bao-Feng, ZHU Han-Min. Pfaffian-Type Soliton Solution to a Multi-Component Coupled Ito Equation[J]. Chin. Phys. Lett., 2014, 31(11): 060203
Viewed
Full text


Abstract