Separation Variable Solution For A Class Of Nonlinear Wave Equation

Nonlinear phenomenon exists widely in mathematics, physics, biology and other fields of modern science. Furthermore, most of these phenomena can be abstracted as a kind of nonlinear equations, so the evolution equations of nonlinear problem play a more and more important role in the main problems which the researchers discuss. In the field of science, for example, a description for all kinds of wave phenomena (such as water waves, electromagnetic waves, light waves, acoustic, etc.) is converted to various related significance of wave equation. Thereby we can explain the phenomenon further. There are many ways of solving nonlinear equations. The method of separation of variables is one of the most practical methods. So far, many methods have been used to study the variable separation solution of nonlinear partial differential equations, including geometry, Ansatz-based method, form variable separation method and so on. In this paper, we use group branch method to study the functional variable separation solution of the nonlinear wave equation It aims to find all set of function about u,K(u), D(v) in each case,so that the original equation has functional separable solution...