Two Types Of Nonlinear (mixed And Degradation) Partial Differential Equations Nature

In recent year, as the mathematical model of physics, chemistry, information science, life science, geography and other fields of science, nonlinear partial differential equations have become the forefront of scientific development and a hot topic. A variety of nonlinear partial differential equations can be roughly divided into two categories. One is integrable and the weak non-integrable. These equations have some better property such as Backlund transformation, Darboux transformation and infinite conservation laws. One form of solitary wave solutions which are widely used has attracted much attention. The other is non-integrable system, whose solutions may be chaotic phenomena.In this paper, we discuss the property of Born-Infeld equations. This class of equations belongs to the first category, which has the form of solitary wave solution.Firstly, this paper summarizes the general solution of Bateman equation, as well as some special properties.Secondly, we consider the type of Born-Infeld equation and give the general solution of this equation via a similar argument to Bateman equation.Thirdly, we give the Cauchy solution of Born-Infeld equation in detail.