Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 293607, 24 pages
Research Article

Extended Mixed Function Method and Its Application for Solving Two Classic Toda Lattice Equations

Center for Nonlinear Science Research, College of Mathematics, Honghe University, Yunnan, Mengzi 661100, China

Received 14 April 2011; Revised 26 May 2011; Accepted 15 June 2011

Academic Editor: Zhengqiu Zhang

Copyright © 2011 Weiguo Rui and Xinsong Yang. 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.


The mixed function method is extended from the ( 1 + 1 ) -dimensional space to the ( 2 + 1 ) -dimensional one, even those forms of exact solution do not exist in ( 1 + 1 ) -dimensional NDDEs. By using this extended method, the Toda lattice and ( 2 + 1 ) -dimensional Toda lattice equations are studied. Some new solutions such as discrete solitary wave solutions, discrete kink and antikink wave solutions, and discrete breather soliton solutions are obtained, and their dynamic properties are discussed.