Existence Of Solitary Wave Solutions For Some Kadomtsev-Petviashvili Equations With Potentials

Since the day the theory came out,soliton theory play a vital role in many physical realms.As an important area of nonlinear discipline,the study of soliton theory attarcts much attention from academic circles,the Kadomtsev-Petviashvili equation in this paper is exactly a major kind of soliton equation.In this paper,we focus on the existence of weak solution of Kadomtsev-Petviashvili equation.Precisely,we will prove that,under Nehari manifold,there exists a weak solution of Kadomtsev-Petviashvili equation with potentials.Chapter 1 is devoted to introduce the development and research status of soliton theory,and the main results of this paper.Chapter 2 introduces some difinitions and lemmas which are related to this paper.Chapter 3 and chapter 4 are where major proofs lay.In chapter 3,what we study is existence of solitary-wave solutions of two dimensional Kadomtsev-Petviashvili equation with two different potentials under Nehari manifold.The periodic potential is one of the potentials.The other one is potential well.In this chapter we firstly introduce the proper function space.Then we apply the thought of mountain pass theorem with Euler Lagrange function to prove existence of solution of equations.In addition,we suggest a new hypothesis about growth of potential which is more natural than before.Because it permit equation concussion within a certain range.What s more,the result of chaper 3 will be generalized to three dimensional Kadomtsev-Petviashvili equation in chapter 4.In chapter 5,we will make a summary of whole paper.