Calculation and analysis of solitary waves and kinks in elastic tubes

TL;DR

This paper analyzes models of wave propagation in elastic tubes, identifying stable solitary waves and kinks, and develops numerical methods to study their behavior and stability.

Contribution

It introduces new methods for calculating and analyzing solitary waves and kinks in elastic tube models, including stability analysis and wave splitting mechanisms.

Findings

Two types of solitary waves identified: stable and unstable.

Null-parametric solitary waves are unstable and can split into kinks.

Kink solutions are stable and may serve as shock structures.

Abstract

The paper is devoted to analysis of different models that describe waves in fluid-filled and gas-filled elastic tubes and development of methods of calculation and numerical analysis of solutions with solitary waves and kinks for these models. Membrane model and plate model are used for tube. Two types of solitary waves are found. One-parametric families are stable and may be used as shock structures. Null-parametric solitary waves are unstable. The process of split of such solitary waves is investigated. It may lead to appearance of solutions with kinks. Kink solutions are null-parametric and stable. General theory of reversible shocks is used for analysis of numerical solutions.