REDUCTIVE PERTURBATION METHOD FOR NONLINEAR WAVE PROPAGATION IN INHOMOGENEOUS MEDIA .I.

The present paper deals with the propagation of waves of small but finite amplitude in slightly inhomogeneous media. The system of equations considered is that of quasi-linear hyperbolic partial differential equations, in which the inhomogeneity is characterized by a slowly varying function of a space coordinate. The original system is reduced, in the lowest step of a perturbation, to a single non-linear equation, which can be integrated by the method of characteristics in case of smooth solutions. © 1969, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.