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

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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.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    I. B. Bakholdin

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  1. I. B. Bakholdin
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Correspondence to I. B. Bakholdin.

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Original Russian Text © I.B. Bakholdin, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 11, pp. 1921–1936.

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Bakholdin, I.B. Numerical study of solitary waves and reversible shock structures in tubes with controlled pressure. Comput. Math. and Math. Phys. 55, 1884–1898 (2015). https://doi.org/10.1134/S0965542515110056

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