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Nonlinear waves in a viscous fluid contained in a viscoelastic tube

  • H. Demiray

Abstract.

In the present work the propagation of weakly nonlinear waves in a prestressed viscoelastic thin tube filled with a viscous fluid is studied. Using the reductive perturbation technique in analyzing the nonlinear equations of a viscoelastic tube and the approximate equations of a viscous fluid, the propagation of weakly nonlinear waves in the longwave approximation is studied. Depending on the order of viscous effects, various evolution equations like, Burgers', Korteweg-de Vries, Korteweg-de Vries-Burgers' equations and their perturbed forms are obtained. Travelling wave type of solutions to some of these evolution equations are sought. Finally, utilizing the finite difference scheme, a numerical solution is presentede for the perturbed KdVB equation and the result is discussed.

Key words. Perturbed Burgers', Korteweg-de Vries equations. 

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Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

  • H. Demiray
    • 1
  1. 1.Isik University, College of Arts and Sciences, Department of Mathematics, Buyukdere Caddesi, 80670 Maslak-Istanbul, TurkeyTR

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