This article is cited in 5 papers

Effect of the pipe curvature on internal elastic wave propagation

V. A. Rukavishnikov, O. P. Tkachenko

Computer Center, Far East Division, Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680000 Russia

Abstract: A mathematical model of internal elastic wave propagation in a bent pipe is developed. For slightly bent pipes, a method is devised for reducing the equations to a lower dimension problem. It is shown that the wave dynamics are described by the Korteweg-de Vries and Klein–Gordon–Fock equations. Thus, the class of problems to which these equations apply is expanded.

Key words: nonlinear waves in bent pipes, mathematical model of wave propagation, Korteweg-de Vries equation, Klein–Gordon–Fock equation, numerical method.

UDC: 519.634

Received: 25.02.2010
Revised: 25.03.2010

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:11, 1886–1894

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