Exact solutions for nonlinear integral member of ​ ​ Kadomtsev-Petviashvili hierarchy differential equations using the modified (w/g)- expansion method

In this paper, we use a new direct method namely modified (w/g )- expansion method to obtain the exact solutions for the integral members of nonlinear Kadomtsev-Petviashvili hierarchy (KPH) equations in physics. In special case when the function w and g are taken particular choices, some families of direct expansion methods are obtained to get the exact solutions for the nonlinear partial differential equations. Based on these interesting results, we further give two forms of expansions via the modified g′/g2- expansion method and modified g′- expansion methods. The solitary wave solutions are derived from the traveling waves solutions when the parameters are taken some special values. This method is simple, and gives many direct new exact solutions.