Nonlinear Magnetoelastic Waves in a Plate

  • Vladimir I. ErofeevEmail author
  • Alexey O. Malkhanov
  • Aleksandr I. Zemlyanukhin
  • Vladimir M. Catson
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


We consider an elastic plate made of conductive material in an external magnetic field. It is shown that the distribution of intense waves in such a system can be described by nonlinear evolution equations, combining the well-known Khokhlov–Zabolotskaya–Kuznetsov and Kodomtsev–Petviashvili model equations. The features of the propagation of two-dimensional nonlinear magnetoelastic waves are analytically and numerically analyzed.


Magnetoelasticity Elastic waves Magnetic field Plate 


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  1. 1.
    Knopoff, L.: The interaction between elastic waves motion and a magnetic field in an electric conductor. J. Geophys. 60, 441–456 (1955)CrossRefGoogle Scholar
  2. 2.
    Bagdasarian, G.E., Danoyan, Z.N.: Electromagnetoelastic Waves. Yerevan State University, Yerevan (2006) (in Russian)Google Scholar
  3. 3.
    Ambartsumian, S.A., Bagdasarian, G.E., Belubekyan, M.V.: Magnetoelasticity of Thin Shells and Plates. Nauka, Moscow (1977) (in Russian)Google Scholar
  4. 4.
    Erofeyev, V.I., Malkhanov, A.O.: Localized magnetoelastic waves formation. Int. Rev. Mech. Eng. 4, 581–585 (2010)Google Scholar
  5. 5.
    Erofeyev, V.I.: Wave Processes in Solids with Microstructure. World Scientific, Singapore (2003)CrossRefGoogle Scholar
  6. 6.
    Erofeyev, V.I., Potapov, A.I., Soldatov, I.N.: Nonlinear Waves in Elastic Bodies with Spatial Dispersion. Gorky Univ Publ., Gorky (1986) (in Russian)Google Scholar
  7. 7.
    Dodd, R.K., Eilbek, J.C., Gibbon, J.D., Morris, H.C.: Solitons and Nonlinear Wave Equations. Academic Press, London (1984)Google Scholar
  8. 8.
    Kydryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos, Solitons and Fractals 24, 1217–1231 (2005)CrossRefGoogle Scholar
  9. 9.
    Press, W.H., Teukolsky, S.L., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C. The Art of Scientific Somputing. Cambrige University Press, Cambridge (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Vladimir I. Erofeev
    • 1
    • 2
    Email author
  • Alexey O. Malkhanov
    • 1
  • Aleksandr I. Zemlyanukhin
    • 3
  • Vladimir M. Catson
    • 3
  1. 1.Nizhny Novgorod Branch of Blagonravov Mechanical Engineering Research Institute of RASNizhny NovgorodRussia
  2. 2.Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia
  3. 3.Saratov State Technical University, SaratovSaratovRussia

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