The Solutions Of Variable-coefficient Nonlinear Equation

This thesis firstly introduced nature of linear and nonlinear and it is importance to physics. Then, general methods of solving of nonlinear equation were introduced and the situation of solving of variable coefficient nonlinear equation was presented intensively. Lastly we researched solving methods of variable coefficient nonlinear equation. It briefly includes several following aspects:Firstly, we introduced connotation of linear and nonlinear and difference between linear and nonlinear differential equations and the role of its in physics. And it was emphasized that the important of solving nonlinear differential equations.Secondly, the general solving methods of nonlinear equations were introduced, such as the Inverse scattering method , Ba|¨cklund transformations method and traveling wave solutions, in order to solving variable coefficient nonlinear equationThirdly, the methods of solving variable coefficient nonlinear equation at present were concluded. And variable separation approach, Jacobi elliptic function, truncated expansion method, improved tanh-function method and Backlund transformations method were introduced intensively.Lastly, at basic of the methods of solving variable coefficient nonlinear equation at present we present a combining method of two methods in solving variable coefficient nonlinear equation, such as methods of Homogeneous Balance and truncated expansion, methods truncated expansion and function reduction, methods Hopf-cole transformation and trial function.