An approximate solution of loaded hyperbolic equation with homogenios boundary conditions

The article proposes a method for solving hyperbolic equation with a spatial variable integral of the natural powers of the unknown function modulus, whereby it is loaded. The author considers an initial boundary value problem with homogeneous boundary conditions. Scalar products of the equation by various functionals and subsequent conversions make it possible to obtain a priori estimates of solutions of the problem in various spaces. By successive integration over the spatial variable the reduction to an ordinary differential equation associated with the initial one is produced. Its approximate solution is sought using a priori estimates that are obtained. Found function leads to the formula that expresses the approximate solution to the original problem through the right parts of the initial conditions.