A Modification of Extended Homoclinic Test Approach to Solve the (3+1)-Dimensional Potential-YTSF Equation

Abstract

By means of the extended homoclinic test approach (EHTA) one can solve some nonlinear partial differential equations (NLPDEs) in their bilinear forms. When an NLPDE has no bilinear closed form we can not use this method. We modify the idea of EHTA to obtain some analytic solutions for the (3+1)-dimensional potential-Yu-Toda-Sasa-Fukuyama (YTSF) equation by obtaining a bilinear closed form for it. By comparison of this method and other analytic methods, like HAM, HTA and three-wave methods, we can see that the new idea is very easy and straightforward.