A method is elaborated for reducing the mixed problem , ,  for a partial differential equation of the hyperbolic type to Cauchy's problem for an infinite system of ordinary differential equations (16). The grounds are given for applying the averaging method of N. M. Krylov and N. N. Bogoliubov to the solution of the resulting system of differential equations. The proposed method is of interest in connection with certain problems of the theory of dynamic stability.
Citation Example:Ilyukhin A. G. Approximate method of solving the mixed problem for a nonlinear partial differential equation containing a small parameter. // Ukr. Mat. Zh. - 1962. - 14, № 3. - pp. 250-259.