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Chin. Phys. B, 2014, Vol. 23(4): 044208    DOI: 10.1088/1674-1056/23/4/044208

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

Zhang Jin-Liang, Wang Hong-Xian
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
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:
About author:  42.81.Dp; 42.65.Tg; 02.30.Jr; 05.45.Yv

Cite this article: 

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

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