Exact Solutions Of An Alice-Bob KP Equation

In order to describe the situation of two or more related events,such as quantum en-tanglement,the Alice-Bob system came into being,because these events are not adjacent or even distant,so the Alice-Bob system is a non-local system.The non-local nonlinear problem has emerged as one of the hot trends in recent years,attracting a lot of scholars to invest energy and research.In order to understand the properties of nonlocal nonlinear equations,it is indispensable to study their solutions,especially the exact solutions.It is a meaningful work to find the physical meaning of the model through exact solutions.This paper combines Alice-Bob system and Kadomtsev-Petviashivili equation to give Alice-Bob's Kadomtsev-Petviashivili(ABKP)system and study the system's PsyPsxTd invariant solution and PsyPsxTd symmetry breaking solution.The whole thesis is composed by five chapters.Chapter 1:In this chapter,we mainly introduce the development history of the soliton and the topic selection work.Chapter 2:In this chapter,we mainly introduce some methods applied in this paper,including bilinear method,similarity solution,CRE method.Chapter 3:In this chapter,we mainly introduce AB-KP system and the principle of AB-BA and give a specific derivation process.Chapter 4:In this chapter,we mainly solve the AB-KP system's PsxpsyTd invariant solutions including PsxpsyTd invariant multi-soliton solutions,PsyPsxTd invariant Painlevé reduction solutions to the ABKP systems,Interaction solutions between soliton and p-wave of the ABKP systems.Chapter 5:In this chapter,we mainly solve PsyPsxTd symmetry breaking solutions of the ABKP system including Symmetry breaking multiple soliton solutions of the ABKP system,PsyPsxTd symmetry breaking cnoidal wave solutions.Chapter 6:In this chapter,we summarize and review the whole paper.