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Nelin. Dinam., 2008, Volume 4, Number 1, Pages 69–86 (Mi nd221)  

This article is cited in 10 scientific papers (total in 10 papers)

Nonlinear evolution equations for description of perturbations in a viscoelastic tube

N. A. Kudryashov, D. I. Sinel'shchikov, I. L. Chernyavsky

Moscow Engineering Physics Institute

Abstract: A quasi-one-dimensional model of flow of a liquid in a viscoelastic tube is considered. A closed system of the nonlinear equations for the description of perturbations of pressure and radius is propose at flow of a liquid in a is viscoelastic tube. For the analysis of system technique of the multiscale method and the perturbation theory is used. The mathematical model was investigated in case of the large Reynolds numbers. In the equation of movement of a wall of a tube the cubic correction to Hooke's law is considered. Families of the nonlinear evolutionary equations for the description of perturbations of the basic characteristics of flow are obtained. Exact solutions of some nonlinear evolution equations are found.

Keywords: viscoelastic tube, nonlinear evolution equations, multiscale method, exact solutions.

Full text: PDF file (187 kB)
UDC:  532.517+539
MSC: 74D10, 35Q35, 34A05
Received: 30.11.2007

Citation: N. A. Kudryashov, D. I. Sinel'shchikov, I. L. Chernyavsky, “Nonlinear evolution equations for description of perturbations in a viscoelastic tube”, Nelin. Dinam., 4:1 (2008), 69–86

Citation in format AMSBIB
\Bibitem{KudSinChe08}
\by N.~A.~Kudryashov, D.~I.~Sinel'shchikov, I.~L.~Chernyavsky
\paper Nonlinear evolution equations for description of perturbations in a viscoelastic tube
\jour Nelin. Dinam.
\yr 2008
\vol 4
\issue 1
\pages 69--86
\mathnet{http://mi.mathnet.ru/nd221}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. S. Abdel Latif, “Simmetriinyi analiz i nekotorye novye tochnye resheniya modifitsirovannogo uravneniya Kortevega–de Friza s peremennymi koeffitsientami, voznikayuschego v arterialnoi mekhanike”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:2 (2011), 42–48  mathnet  crossref
    2. Kudryashov N.A., Ryabov P.N., “Properties of nonlinear waves in an actively-dissipative dispersive medium”, Fluid Dynamics, 46:3 (2011), 425–432  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    3. Abdel Latif Mokhamed Soror, “Chislennye issledovaniya uedinennykh voln v napolnennykh zhidkostyu uprugikh trubkakh”, Estestvennye nauki, 2011, no. 2, 188–192  elib
    4. Kudryashov N.A., Kochanov M.B., “Quasi-Exact Solutions of Nonlinear Differential Equations”, Appl. Math. Comput., 219:4 (2012), 1793–1804  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kudryashov N.A., “Quasi-Exact Solutions of the Dissipative Kuramoto-Sivashinsky Equation”, Appl. Math. Comput., 219:17 (2013), 9213–9218  crossref  mathscinet  zmath  isi  elib  scopus
    6. Barlukova A.M., Cherevko A.A., Chupakhin A.P., “Traveling Waves in a One-Dimensional Model of Hemodynamics”, J. Appl. Mech. Tech. Phys., 55:6 (2014), 917–926  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. G. A. Shaposhnikova, “Influence of the velocity profile on the properties of equations averaged over the cross section for the liquid flow in flexible-wall tubes”, Dokl. Phys., 59:7 (2014), 326–329  crossref  crossref  mathscinet  isi  elib  elib  scopus
    8. Kumar R., Gupta R.K., Bhatia S.S., “Lie Symmetry Analysis and Exact Solutions For a Variable Coefficient Generalised Kuramoto-Sivashinsky Equation”, Rom. Rep. Phys., 66:4 (2014), 923–928  isi
    9. N. A. Kudryashov, “Method of the logistic function for finding analytical solutions of nonlinear differential equations”, Model. i analiz inform. sistem, 22:1 (2015), 23–37  mathnet  mathscinet  elib
    10. Kudryashov N.A., “Painlevé Analysis and Exact Solutions of the Fourth-Order Equation For Description of Nonlinear Waves”, Commun. Nonlinear Sci. Numer. Simul., 28:1-3 (2015), 1–9  crossref  mathscinet  isi  elib  scopus
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