The Successive Approximations Method Of The Solutions For A Class Of Non-linear Wave Equations

In this paper, we discuss a class of non - linear partial differential equations such as:(where f(x,t,u)is non ?linear function on u). This is a one ?dimensional nonlinear wave equation. The formulas of iterative solutions for this equation are obtained by using the successive approximations method. The theorem on the existence and uniqueness of the solution for this problem are also theoretically proved.