Characteristic method and its some applications in solving partial differential equations

For one order linear hyperbolic partial differential equation,we aim to obtain the analytic solution of the Cauchy problem,so we propose characteristic method.The fundamental idea is to transform the Cauchy problem of partial differential equation into the corresponding problem of order differential equation.By solving the order differential equation,we can obtain the solution of the former partial differential equation.Through studying method of characteristics,we get the general steps of solving the Cauchy problem of one order linear hyperbolic partial differential equation.Furthermore,we give some applications.