Abstract
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.
Highlights
In 1, motivated by the structures of the exact solutions obtained from Darboux transformation, the authors constructed the mixed function method in 1 1 -dimensional space
Discrete Dynamics in Nature and Society saved. We notice that this extended method is as powerful as the other symbolic computation methods such as tanh-function method, sine-cosine function method, exp-function method, Jacobian elliptic function method, G /G -expansion method, and Adomian decomposition method, and these methods please refer to 2–18 and references cited therein are popular tools in the field of the nonlinear differential-difference equations
We introduced an extended method based on the mixed function method
Summary
In 1 , motivated by the structures of the exact solutions obtained from Darboux transformation, the authors constructed the mixed function method in 1 1 -dimensional space. They studied the generalized Hybrid lattice equation and the two-component Volterra lattice equation by using this method, they obtained some new exact solutions such as discrete solitary wave solutions and kink wave solutions. By using the exp-function method, Zhu 7 studied 2 1 -dimensional Toda lattice equation and obtained some exact solutions of exp-function type.
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