Exact Solutions Of Several Variable Coefficients Nonlinear Equations

This dissertation attempts to give several methods for solving the variable coefficients nonlinear equations and we focus our attention on the function transformation method. Function transformation method is a direct and effective method, by which one not only can get the Jacobi elliptic function solutions and the hyperbolic function solutions, but also can get the triangle function solutions. In chapter 1, the concept of solitons, the significance of studying soliton theory and the methods for obtaining exact solutions in soliton theory are introduced. In the meantime, the main work of this dissertation is also briefly introduced. In chapter 2, by using the first kind of transformation, the variable coefficients nonlinear equations are reduced to nonlinear ordinary differential equations (NLODE). Several exact soliton-like solutions for the variable coefficients KdV equation, variable coefficients mKdV equation, variable coefficients KP equation, variable coefficients nonlinear Schr?dinger equation for optical fiber, variable coefficients combined KdV equation and variable coefficients coupled KdV equation are obtained through use of the corresponding reduced NLODES. In chapter 3, by using the second kind of transformation, several exact soliton-like solutions for a type of variable coefficients generalized KdV-Burgers equation are obtained. In chapter 4, by using the third kind transformation, several exact soliton-like solutions for the variable coefficients KdV equation are obtained.