Calculation and analysis of solitary waves and kinks in elastic tubes

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.