Approximate solution of the Cauchy problem for a hyperbolic equation with a nonlinear source

An approximate method is described for the Cauchy problem for a nonlinear hyperbolic equation. The method reduces the problem to an integro-differential equation of 2nd kind that can be solved iteratively. Minimum smoothness conditions are imposed on the nonlinear coefficient. Unique solvability is proved. __________ Translated from Prikladnaya Matematika i Informatika, No. 19, pp. 41–55, 2004.