This article is cited in 9 papers

Numerical study of solitary waves and reversible shock structures in tubes with controlled pressure

I. B. Bakholdin

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: Methods for computing and analyzing solutions for a model of a tube with elastic walls in the case of controlled internal pressure is developed. A membrane model or a plate model is used for the tube walls. Numerical methods are applied. The Boussinesq equations are used to describe waves near the transition to the instability zone of homogeneous states and to verify the numerical methods. Solitary waves and soliton shock structures for these equations are studied. The Boussinesq equations are analyzed and generalized. Next, the same methods are applied to the complete equations. Solitary waves and reversible shock structures (generalized kinks) are studied. The stability of the solitary waves is analyzed by finding an eigenfunction. The kinks are studied using general methods of the theory of reversible shocks.

Key words: waves in tubes, elasticity controlled pressure, dispersion, nonlinearity, solitary wave, kink, shock structure, numerical analysis, Boussinesq equation.

UDC: 519.634

MSC: Primary 76B25; Secondary 74J35

Received: 10.12.2014
Revised: 23.04.2015

DOI: 10.7868/S0044466915110058

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:11, 1884–1898

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