Задача Коши для нелинейных уравнений с гиперболическим оператором высокой степени

It is consider a nonlinear integro-differential equation with nonlinear hyperbolic operator of the higher order with initial value conditions. It is proposed in this paper a technique based on the characteristics method. This technique allows, moving to a new variable, provide a partial differential equation as an ordinary differential equation describing the change of unknown function along the characteristics. The study of the Cauchy problem reduces to the study of nonlinear Volterra integral equation. By the method of successive approximations it is proved the existence and uniqueness of the solution of this problem.