Exact solutions and linear stability analysis for two-dimensional Ablowitz–Ladik equation

doi:10.1088/1674-1056/23/4/044208

Abstract The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyperbolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the (G'/G)-expansion method, and the effects of the parameters (including the coupling constant and other parameters) on the linear stability of the exact solutions are analysed and numerically simulated.

Keywords: two-dimensional Ablowitz-Ladik equation linear stability exact solution numerical simulation

Received: 28 May 2013
Revised: 14 July 2013
Accepted manuscript online:

PACS:	42.81.Dp	(Propagation, scattering, and losses; solitons)
	42.65.Tg	(Optical solitons; nonlinear guided waves)
	02.30.Jr	(Partial differential equations)
	05.45.Yv	(Solitons)

Fund: Project supported by the Basic Science and the Front Technology Research Foundation of Henan Province, China (Grant Nos. 092300410179 and 122102210427), the Doctoral Scientific Research Foundation of Henan University of Science and Technology, China (Grant No. 09001204), the Scientific Research Innovation Ability Cultivation Foundation of Henan University of Science and Technology, China (Grant No. 011CX011), and the Scientific Research Foundation of Henan University of Science and Technology (Grant No. 2012QN011).

Corresponding Authors: Zhang Jin-Liang
E-mail: zhangjin6602@163.com

About author: 42.81.Dp; 42.65.Tg; 02.30.Jr; 05.45.Yv

Cite this article:

Zhang Jin-Liang (张金良), Wang Hong-Xian (王红县) Exact solutions and linear stability analysis for two-dimensional Ablowitz–Ladik equation 2014 Chin. Phys. B 23 044208

[1]	Kevrekidis P G 2009 The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives (Berlin: Springer-Verlag) p. 3
[2]	Kuznetsov E A, Rubenchik A M and Zakharov V E 1986 Phys. Rep. 142 103
[3]	Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press) p. 200
[4]	Gu C H 1990 Soliton Theory and Its Application (Hangzhou: Zhejiang Publishing House of Science and Technology) p. 160
[5]	Miura M R 1978 Bäcklund Transformation (Berlin: Springer-Verlag) p. 185
[6]	Hirota R 1971 Phys. Rev. Lett. 27 1192
[7]	Hu X B and Tam H W 2000 Phys. Lett. A 276 65
[8]	Sun M N, Deng S F and Chen D Y 2005 Chaos, Solitons and Fractals 23 1169
[9]	Parkes E J and Duffy B R 1996 Comput. Phys. Commun. 98 288
[10]	Wang M L 1995 Phys. Lett. A 199 169
[11]	Wang M L, Zhou Y B and Li Z B 1996 Phys. Lett. A 216 67
[12]	Zhang J L, Wang Y M, Wang M L and Fang Z D 2003 Chin. Phys. 12 245
[13]	Dai C Q, Cen X and Wu S S 2008 Comput. Math. Appl. 56 55
[14]	Soto-Crespo J M, Akhmediev N and Ankiewicz A 2003 Phys. Lett. A 314 126
[15]	Chow KW, Conte R and Xu N 2006 Phys. Lett. A 349 422
[16]	Malomed B and Weinstein M I 1996 Phys. Lett. A 220 91
[17]	Malomed B A, Crasovan L C and Mihalache D 2002 Physica D 161 187
[18]	Pelinovsky D E, Kevrekidis P G and Frantzeskakis D J 2005 Physica D 212 1
[19]	Chong C and Pelinovsky D E 2011 Discrete and Continuous Dynamical Systems, Series S 4 1019
[20]	Dai C Q and Zhang J F 2006 Opt. Commun. 263 309
[21]	Huang W H and Liu Y L 2009 Chaos, Solitons and Fractals 40 786
[22]	Maruno K, Ohta Y and Joshi N 2003 Phys. Lett. A 311 214
[23]	Maruno K, Ankiewicz A and Akhmedievc N 2003 Opt. Commun. 221 199
[24]	Maruno K, Ankiewicz A and Akhmedievc N 2005 Phys. Lett. A 347 231
[25]	Aslan I 2011 Phys. Lett. A 375 4214
[26]	Aslan I 2009 Appl. Math. Comput. 215 3140
[27]	Kevrekidis P G, Herring G J, Lafortune S and Hoq Q E 2012 Phys. Lett. A 376 982
[28]	Khare A, Rasmussen K O, Samuelsen M R and Saxena A 2005 J. Phys. A: Math. Gen. 38 807
[29]	Khare A, Rasmussen K O, Samuelsen M R and Saxena A 2011 Phys. Scr. 84 065001
[30]	Zhang J L and Liu Z G 2011 Commun. Theor. Phys. 56 1111
[31]	Zhang J L, Liu Z G, Li S W and Wang M L 2012 Phys. Scr. 86 015401
[32]	Wang M L, Li X Z and Zhang J L 2008 Phys. Lett. A 372 417
[33]	Wang M L, Zhang J L and Li X Z 2008 Appl. Math. Comput. 206 321
[34]	Guo S M and Zhou Y B 2010 Appl. Math. Comput. 215 3214

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Exact solutions and linear stability analysis for two-dimensional Ablowitz–Ladik equation

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