Non-linear patterns of bends and solitons on surfaces of loaded shells

The study develops special variants of perturbation theory to reduce the three-dimensional dynamic non-linear equations for plates and cylindrical shells to the simpler two-and one-dimensional ones. New substantially non-linear models are obtained that correctly account for boundary conditions on the surfaces of the samples, both geometric and physical non-linearity of the media and interactions between the longitudinal and the transverse modes of deformation. Basing on these model patterns composed of dents and new types of solitons on the surfaces of the elastic systems are described.