Numerical simulation of bulk solitons in elongated shells

A mathematical model, proposed recently to describe longitudinal waves in the nonlinearly elastic thin-walled cylindrical shell, is used to derive an equation for the longitudinal strain component in case of variable geometrical and physical properties of the shell. To solve the Cauchy problem for this equation the finite difference scheme is proposed, that satisfies the conservation laws of “pseudo-mass” and “pseudo-energy” for a solitary wave solution. A numerical simulation, based on this scheme, is performed to study evolution of the strain soliton in a cylindrical shell with variations of both cross section of the shell and the physical properties of the material.