(3 +1)-dimensional Kp Equation Periodic State And Chaotic Behavior,

In this thesis, we consider(3+1)-dimensional Kadomtsev-Petviashvili equation (KP), as followingAs we know, periodic, homoclinic and chaotic behaviour of (3+1)-dimensional Kadomtsev-Petviashvili equation has significant applied background,on physics and mathematics.Since Lorentz published the thesis,"Periodic flow of determinism" in 1963. Non-linear science which reveals the common nature of the basic characteristics and law of motion has rapidly developed. In the recent 20 years, important reason of the rapid development of non-linear science is that chaotic motion was found.while describing the various types of power systems. Chaotic motion is a common, Thus, many problems on physics and mechanics can be attributed to the disturbance with a weak cycle, that has homoclinic orbit or heteroclinic loop of second-order ordinary differential equations.In this thesis, using Melnikov method and character of the Hamiltion system,we obtain homoclinic orbit, periodic orbit and systematic chaos of KP.What is more,we know that melinikov-type functions can be used to establish homoclinic orbits of integrable system under the condition of disturbances and phase space.This thesis consists of three chapters to study periodic states and chaotic behavior of (3+1)dimensional KP equation.In chapter 1.we give some basic concepts and properties of partial differential equation.In chapter 2.we study the periodic states and chaotic behavior of (3+1) dimensional KP equation.In chapter 3.we expand the application of (3+1) dimensional KP equation.