Discrete tanh method for nonlinear difference-differential equations

By introducing a simple difference equation to deduce the difference terms and a simple differential equation to deduce the differential terms, we proposed an unified algebraic method for constructing exact solutions to difference-differential equations (DDEs). This method could give many kinds of exact solutions including soliton solutions expressed by hyperbolic functions, periodic solutions expressed by trigonometric functions and rational solutions in a uniform way if solutions of these kinds exist. In this paper, we also give a generalization of the method to determine the degree of DDEs, and compared with the creativity work of D. Baldwin et al. [D. Baldwin, Ü. Göktas, W. Hereman, Comput. Phys. Comm. 162 (2004) 203–217] through the discrete Hybrid equation.