Axisymmetric Nonlinear Modulated Waves in a Cylindrical Shell

A quasi-hyperbolic equation is derived that simulates the axisymmetric propagation of bending waves in a cylindrical shell, which interacts with a nonlinearly elastic medium. With the correct asymptotic procedure, the study of a wave process reduces to analysis of a nonlinear Schrödinger equation. It is established that the development of modulation instability requires a “soft” nonlinearity of the medium surrounding the shell. Operating modes that allow the propagation of stable light envelope solitons are revealed.