ON THE APPROXIMATE-ANALYTIC METHOD OF SOLVING A NONLINEAR HYPERBOLIC EQUATION WITH HOMOGENEOUS INITIAL CONDITIONS

The paper presents a method for solving a mixed problem with homogeneous initial conditions for a loaded hyperbolic equation with an integral natural degree modulus of unknown function. An approximate solution is sought for by means of a priori estimates of the solution to the problem. A formula expressing the solution through the solution to the ordinary differential equation associated with the initial loaded equation is obtained.