Russian Journal of Mathematical Physics

, Volume 25, Issue 4, pp 459–469 | Cite as

Influence of the Elastic Base of a Basin on the Propagation of Waves on the Water Surface

  • S. Yu. DobrokhotovEmail author
  • O. L. Tolstova
  • S. Ya. Sekerzh-Zenkovich
  • C. A. Vargas


A layer of an ideal liquid located on an elastic half-space (with a flat unperturbed boundary) is considered in the linear approximation. At the zero time moment, a localized perturbation of the displacement vector occurs in the elastic half-space, and this perturbation, after some time, leads to a modification (perturbation) of the interface between the water and the crust, which, in turn, leads to a localized perturbation on the surface of the liquid and to the occurrence of surface waves. We are interested in the following question: to what extent does getting rid of the stiffness of the bottom and replacing it by an elastic base influence the speed of propagation of the front of the long wave and its profile under the assumption that the initial perturbation is given immediately on the free surface of the liquid?


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • S. Yu. Dobrokhotov
    • 1
    • 2
    Email author
  • O. L. Tolstova
    • 2
    • 3
  • S. Ya. Sekerzh-Zenkovich
    • 1
  • C. A. Vargas
    • 4
  1. 1.Ishlinsky Institute for Problems in Mechanics RASMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Steklov Mathematical InstituteMoscowRussia
  4. 4.Institute of Applied Mathematics and Systems, FENOMECUniversidad Nacional Autonoma de Mexico (UNAM)MexicoMexico

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