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

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.