Finding Solutions And Research On Methods For Nonling

In this paper, it mainly aims at some nonlinear partial differential equations with significant physical background. According to the soliton theories and methods in being, for instance, homogeneous balance method, function transformation method, exponential function expansion method, hyperbolic tangent function method, modified Jacobi elliptic function expansion method and so forth,on the basis of tasks had been done,this paper obtains their numerous new solitary wave solutions and other form exact solutions under the guidance of mathematics mechanization and by means of symbolic computation system Mathematica 5.0. The following is the structure of this article:The first chapter describes the development situation of nonlinear partial differential equations to find the solutions,which includes the introduction to the concept of nonlinear partial differential equations and the results from previous to construct exact solutions of partial differential equations.The second chapter describes the profile of the soliton and the practical significance to study soliton,listing several common types'solitons,which be done a comparison between three-dimensional and flat graphics,generalizing a large number of different types partial differential equations studied widely.The third chapter gives the definition of traveling wave solution. Firstly it finds the Tanh form solutions of Burgers equation and combined KdV equation,then introducing the origin of the classical KdV equation and finding its traveling wave solutions in detail. Lastly the paper aims at KP equation to find the solutions by using auxiliary Riccati equation method.The fourth chapter is the focal point in this paper. It gives the definition of quasi solution and describes the steps of the homogeneous balance method in detail. With this method, to find the solutions for KdV-Burgers;New function transformation is applied to variable coefficients KdV equation for finding the solutions ,which be plotted graphics by using Mathematica;We get the different form solutions to the coupled KdV equations set with F-expansion method, including elliptic function, trigonometric function, hyperbolic function, power function solutions.The fifth chapter mainly summarizes the work done in this paper and focuses on pointing out the new outlook to the future study of the subject.Currently, it has been done plant of studies in practice and theory about soliton, especially in the aspect of finding solutions to nonlinear partial differential equations. But acquisition to the exact solutions is a progress of larger difficulty and high skill so as to it gradually becomes an important issue studied commonly to solve different equations with different methods. Based on this purpose,the paper more systematic and in-depth studies part equations with actual physical meaning on the basis of summarizing various nonlinear partial differential equations. It gets many new results in light of results had been obtained. The new results signify that,firstly, it simulates graphics of the different types'solitons and exact solutions to many equations with software Mathematica;secondly,it obtains lots of new exact solutions to different equations with different methods, enriching and developing the contents of methods'study in nonlinear partial differential equations.