New Exact Solutions Of Klein-Gordon Equations

Partial differential equations, which is originated in the 18th century, belong to the area of Analytics, and is a branch of science appeared shortly after the emergence of calculus. With the extension of the phenomenon of physical science researching in both breadth and depth, the theory and application of differential equation rapidly become a "math center" to promote the development of other branches of mathematics. Partial differential equations , relevant to a large number of practical problems, becomes the frontier of natural science and a research focus, is one of the main research direction of the foundation mathematics and applied mathematics, and is of great theoretical and practical significance. Therefore people become more and more interested in researching and exploring it. One of the basic problems of partial differential equations is to find its precise solution, which, to a large extent, helps people to understand the nature of natural phenomena, so it is particularly important to look for exact solutions of partial differential equations.In this paper, we discuss how to find the precise solutions of Klein-Gordon equation , which is in close contact with the physical problems and plays an important role in the study of the solution theory.In this paper, we discuss how to use F-expansion method, Jacobi elliptic function method and its extension and exponential function method to find the precise solution of nonlinear Klein-Gordon equation, meanwhile we respectively note the advantages of Jacobi elliptic function expansion method and exponential function method in solving partial differential equations.