Accurate The Potential Kadomstev-petviashvili Equation Soliton Solution

The soliton equation is one of the most prominent subject in the fields of nonliear science. In this paper, we consider an important soliton equation. There are sevral systematic approches to obtain solutions of soliton equation. The direct method has been proved to be one of the most important method in soliton theory. The nonlinear differential equations are transformed into a type of a bilinear differential equations in Hirota method. Then, to find an exact solution by a perturbation method.In this thesis ,there are five parts. In section one ,we mainly introduce backgrouding knowledge and the essentials of the direct methods in soliton theory.In section two ,we consider the Potential Kadomstev-Petviashvili soliton equation, then the Potential Kadomstev-Petviashvili soliton equation can be transformed into bilinear differential equations through logarithmic transformation. The logarithmic transformation are:u=(12α)/β(lnf)xand the bilinear differential equations are:(D_xD_t+βD~4_x+γD~2_y)f·f=0find the exact N soliton solutions by a perturbation method.In section three ,we consider the Potential Kadomstev-Petviashvili soliton equation.The exact single, double and N soliton solutions are obtained by the Hirota method.In section four, we got the Wronskian solutions.In section five, we got the grammian solutions.