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Discrete Dynamics in Nature and Society
Volume 2012, Article ID 652076, 19 pages
Research Article

A New Discrete Integrable System Derived from a Generalized Ablowitz-Ladik Hierarchy and Its Darboux Transformation

1Junior College, Zhejiang Wanli University, Ningbo 315100, China
2College of Mathematics, Honghe University, Mengzi 661100, China
3College of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, China

Received 9 October 2011; Accepted 4 December 2011

Academic Editor: Zuo Nong Zhu

Copyright © 2012 Xianbin Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We find an interesting phenomenon that the discrete system appearing in a reference can be reduced to the old integrable system given by Merola, Ragnisco, and Tu in another reference. Differing from the works appearing in the above two references, a new discrete integrable system is obtained by the generalized Ablowitz-Ladik hierarchy; the Darboux transformation of this new discrete integrable system is established further. As applications of this Darboux transformation, different kinds of exact solutions of this new system are explicitly given. Investigatingthe properties of these exact solutions, we find that these exact solutions are not pure soliton solutions, but their dynamic characteristics are very interesting.