Explicit Solutions of Integrable Variable-coeffcient Cylindrical Toda Equations

Integrable cylindrical Toda lattice equations are proposed by utilizing a generalized version of the dressing method. A compatibility condition is given which insures that these equations are integrable. Further, soliton solutions for new type equations are shown in explicit forms, including one soliton solution and two soliton solutions, respectively.

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

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.