Solitary waves on a cylinder shell with liquid

Abstract

Traditionally, non-linear wave propagation has been under consideration in classical hydro-dynamics, as well as in such areas of physics like optics and plasma theory. By contrast, we study the same problem within the framework of deformable solid body theory. Specifically, non-linear wave propagation is considered in a basic model of pipeline. We make use of classical non-linear thin elastic shell equilibrium equations along with Euler equations for a non-compressible non-viscous liquid. A soliton-type asymptotic solution is constructed. The existence of the single soliton on the “dry” shell is proved; while on the “filled up” shell there exist exactly two solitons. The behavior of these solutions was studied under the inter-connectedness factor, numerical results are provided. The results obtained may be put in practice, like construction engineering.