Research And Solution Of The Nonlinear Evolution Equations Is Symmetry

Of the nineteenth century, people began to study the nonlinear partial differential equations (PDEss). Since1960, the research of nonlinear developed rapidly. Study of PDEss as a new interdisciplinary subject, the contents of it richer and richer. One of important achievements is variety of methods which found accurate solutions for nonlinear partial differential equations, especially in isolated of the wave solutions. For example, Inverse scattering method, hom-egeneous balancing method, Darboux transformation Hirota bilinear method, Tanh function method, homoclinic test technique, F-expansion method eta. These methods have been successful got a lot solutions of nonlinear partial differential accurate equations. This article on the basis of solution theory and method of study and research, improve and applied the method to obtain several of the equations new accurate solution. This paper with a total of four chapters, Content as follows.The first chapter:Introduce soliton theory research background and their development. To elaborate integrability of equation, introduced several ways of the solution of PDEss.The second chapter:First application homoclinic test technique, introduce test function, combination of Hirota bilinear method determines the pending function of the test function. Then to find the solution of the (2+1)-dimensional Boussinesq equation. Using extended homoclinic test technique we obtain new accurate solution of (2+1)-dimensional Boussinesq equation. Application software of computer symbol matlab draw images of solutions. Second used in the solution of equations of the F-expansion method, to solve the equations with the solutions of auxiliary equation, structure of solutions be enriched. Finally, solve Hirota-Satsuma equations by extended Tanh function method. Solve MEW equation by another extended Tanh function method.The third chapter:gave a detailed account Lie group theory. First of all, clear definitions and important theorem, introduce how to use the Lie group theory about reduction and solution. Then application method to Lie and software of computer symbol maple obtain infintesimal generator and Lie symmetry of Boussinesq-Burgers equation. Through different select values situation, obtain reduction of equations. Obtain Lie group of transformations by solve the initial value problems of the equations and obtain new solutions of the equations.The furth chapter:Summary of the full paper.