Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid

  • Oxana Kurkina
  • Andrey Kurkin
  • Efim Pelinovsky
  • Yury Stepanyants
  • Tatiana Talipova
Part of the Mathematics of Planet Earth book series (MPE, volume 6)


We present an example of systematic use of asymptotic methods for the description of long waves at the interface between two fluids of different densities. The governing equations for weakly nonlinear long interfacial waves are consistently derived for a general case of nonpotential flow and taking into account surface tension between two layers. Particular attention is given to the situations when some terms in the resulting fifth order KdV-type evolution equation become small, vanish, or change their sign.


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This study was financially supported by the state task program in the sphere of scientific activity of the Ministry of Science and Higher Education of the Russian Federation (projects No 5.4568.2017/6.7 and 5.1246.2017/4.6), grant of the President of the Russian Federation (NSh-2685.2018.5), Program “Nonlinear Dynamics” of the Russian Academy of Sciences and grants of the Russian Foundation for Basic Research (RFBR No 18-02-00042, 19-05-00161).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Oxana Kurkina
    • 1
  • Andrey Kurkin
    • 1
  • Efim Pelinovsky
    • 2
    • 3
    • 4
  • Yury Stepanyants
    • 4
  • Tatiana Talipova
    • 1
    • 2
  1. 1.Nizhny Novgorod State Technical University n.a. R.E. AlekseevNizhny NovgorodRussia
  2. 2.Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS)Nizhny NovgorodRussia
  3. 3.National Research University–Higher School of EconomicsNizhny NovgorodRussia
  4. 4.University of Southern QueenslandToowoombaAustralia

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