Of Nonlinear Diffusion Equation With Convection Term And The Source Of The Variable Separation Solutions

In this paper, we considered the separable solutions to the (1+1)-dimensional nonlinear reaction-diffusion-convection equation with the group fo-liation method. The paper is organized as follows:In chapter1, the status and main applications of the nonlinear theory are recommended, then, the method of variable separation of the background, de-velopment and current situation are introduced. And we give a solution to solve the separation of variables case. In chapter2, we briefly introduce some main types of separable solutions and the method of group foliation. Then the main content of this paper is presented.In chapter3, we considered the separable solutions to the (1+1)-dimensional nonlinear reaction-diffusion-convection equation with the group foliation method, we obtain the ordinary variable separation solutions, that the coefficient functions satisfy the relations, and in each case the functions of the variable u are obtained; obtained in the form of the equation satisfy the function of separation of variables solution. Obtained in the form of functional separable solutions and the relations with the functions depend on u.