Traveling wave packets in a non-homogenous narrow medium bounded by a surface of revolution

The process of wave propagation in an infinitely long non-homogeneous narrow medium (waveguide) bounded by a surface of revolution is considered. An asymptotic solution of thewave equation is constructed in the form of localized families of short waves (the wave packets) running in the longitudinal direction, the wave length being of the same order as the characteristic width of the waveguide. As a particular case, the found solution permits to study free oscillations of the medium near the cross-section having the maximum diameter. The effects of reflection of the traveling wave packets from some cross-sections and a localization of the wave processes in a neighborhood of the section with the maximum diameter are revealed.