Nonlocal Symmetry,Interaction Solutions And Conservation Laws Of The Partial Nonlinear Equations

Nonlinear partial differential equation is a subject which has a long history.it is also a very important mathematical model that appears in various fields of science.In this paper,three problems of the nonlinear partial differential equations are studied by using computer algebra as auxiliary tool.They are nonlocal symmetry,interaction solutions and conservation laws.The contents of this paper are divided into the following five parts:In the first chapter,we briefly introduce some methods to obtain interaction solutions and conservation laws of the nonlinear partial differential equations.Then the main contents of this paper are also clarified.In the second chapter,the basic theoretical knowledge of the thesis is introduced in detail.In the third chapter,it presents the(2+1)-dimensional Kaup-Kupershmidt system,then nonlocal symmetry and interaction solutions for the(2+1)-dimensional Kaup-Kupershmidt system are given.In the fourth chapter,the potential Kadomtsev-Petviashvili equation with p-power is introduced firstly,then we apply the Noether method to construct conservation laws of this equation.In the fifth chapter,we summarize the whole text and put forward the outlook.