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Z. Naturforsch. 67a, 21 (2012)
doi:10.5560/ZNA.2011-0063
Construction of Quasi-Periodic Wave Solutions for Differential-Difference Equation
Y. C. Hon1 and Qi Wang2
1 Department of Mathematics, Tat Chee Avenue 80, City University of Hong Kong, Hong Kong, PR China
2 Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, PR China
Received August 25, 2011
Reprint requests to: Q. W.; E-mail: wangqee@gmail.com
Based on the use of the Hirota bilinear method and the Riemann theta function, we develop in this paper a constructive method for obtaining explicit quasi-periodic wave solutions of a new integrable generalized differential-difference equation. Analysis on the asymptotic property of the quasi-periodic wave solutions is given, and it is shown that the quasi-periodic wave solutions converge to the soliton solutions under certain conditions.
Key words: Hirota Bilinear Method; Riemann Theta Function; Quasi-Periodic Wave Solutions.
PACS numbers: 03.65.Ge; 02.30.Ik
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