New Variable Separation Solutions To The (2+1)-dimensional Nonlinear Evolutional Equations

With the linear theory being perfect increasingly, the nonlinear science widely appearing in almost all the scientific fields has been the focus for the researchers. So it's inevitably to come into contact with various nonlinear equations which describe the nonlinear systems for the researchers. As a result, to deal with the nonlinear equations becomes the crucial and difficult work for the researchers in the nonlinear field.It is well known that there isn't an uniform method to deal with the nonlinear equations, which is different from the linear equations. And one method usually can't get all kinds of solutions. For the nonlinear PDE, there are many effective methods to obtain exact solutions, such as the classical and nonclassical Lie symmetry, direct method, geometric method, generalized condition symmetry, formal variable separation approach and multi-linear variable separation approach and so on.In this article, we utilize an improved multi-linear variable separation approach to study a sort of the (2+l)-dimensional nonlinear evolutional equations. And through further improving the method, We obtain some new exact solutions which include the variable separation solutions.In the chapter 1, we introduce some methods to study the exact solution of nonlinear partial differential equations.In the chapter 2, we utilize an improved multi-linear variable separation approach and further improve the method to study a sort of the (2+1)-dimensional nonlinear evolutional equations. And some new exact solutions which include the variable separation solutions can be obtained.In the chapter 3, we give the summary and expectations of the article.