Repeated Homogeneous Balance Method In Soliton Equations Solving

Content: This dissertation has mainly done the following aspects research: the basic method to solve Nonlinear partial differential. and its application of non-linear mathematical physics. By means of the homogeneous balance method one of method was used to given exact traveling wave solutions about nonlinear evolution equation model. but the transformation equation-Riccati equation is one of nonlinear equation and difficult to solve, so to some extent the way of the homogeneous balance method had limit the solution. In this paper, repeated homogeneous balance method and function construction method were used to solve non-linear of partial differential equation ,which is the homogeneous balance method for solving equations-Riccati equation and the transformation simplifies the nonlinear ordinary differential equations, In this way, many forms of exact traveling wave solution about nonlinear partial differential equations could obtained. Many forms of exact solutions are the new solutions, which cover the results obtained by other methods. So to a certain extent solve the above-mentioned deficiencies.Chapter 1 is to introduce the history and development of the solitary theory, and the application in the nature sciences, research statue and method, as well as domestic and foreign scholars in these areas work, and some of the results have achieved.Chapter 2 describes some of the basic methods, which are used to solve the nonlinear partial differential equations. such as: nonlinear evolution equation of the solitary wave solutions, the direct integration method and observation of trial method, Lax integrable and soliton equations, Ba cklund transformation method, Hirota bilinear derivative method and Darboux transformation method, homogeneous balance method and first-time integration method. And give a brief overview of the various methods of uniqueness.Chapter 3 the focus of this chapter based on the nonlinear evolution equation algebra, algorithm-based, mechanized guiding ideology, put forward using Repeated homogeneous balance method, and promote Tanh function construct method. and the new method is applied to soliton equations-Chaffee-Infante. In this way a large number of exact traveling wave solutions received. These results include the results obtained using other methods, as well as a large number of other forms of new solutions.Chapter 4 Repeated homogeneous balance method, and the promotion of a function of tectonic deformation method is applied to soliton equations Boussinesqâ… .And a large of the exact traveling wave solutions about soliton equations obtained.