Generalized method to construct the solitonic solutions to (3+1)-dimensional nonlinear equation

A generalized method with computerized symbolic computation, which is called the generalized extended tanh-function method, is presented for the nonlinear equations of mathematical physics (NEMPs). Compared with most of the existing tanh-function method, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEMPs. Make use of the method, we study the (3+1)-dimensional potential-YTSF equation and obtain rich new families of the exact solutions, including the nontraveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions.