Nonlinear and linear wave phenomena in narrow pipes

Phenomena arising in the course of wave propagation in narrow pipes are considered. For nonlinear waves described by the generalized Webster equation, a simplified nonlinear equation is obtained that allows for low-frequency geometric dispersion causing an asymmetric distortion of the periodic wave profile, which qualitatively resembles the distortion of a nonlinear wave in a diffracted beam. Tunneling of a wave through a pipe constriction is investigated. Possible applications of the phenomenon are discussed, and its relation to the problems of quantum mechanics because of the similarity of the basic equations of the Klein-Gordon and Schrödinger types is pointed out. The importance of studying the tunneling of nonlinear waves and broadband signals is indicated.