Variable-coefficient discrete tanh method and its application to (2+12+1)-dimensional Toda equation

In this Letter, a variable-coefficient discrete tanh method is proposed for solving nonlinear differential–difference equations. With the aid of symbolic computation, we choose a (2+12+1)-dimensional Toda equation to illustrate the validity and advantages of the method. As a result, hyperbolic function solutions, trigonometric function solutions and rational solutions with arbitrary functions are obtained. It is shown that the proposed method provides a powerful mathematical tool for nonlinear differential–difference equations in mathematical physics.