Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Abstract

With the aid of the symbolic computation, we present an improved ( G ′ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.