Kadomtsev-Petviashvili and (2+1)-dimensional burgers equations in the Bénard problem

  • R. A. Kraenkel
  • S. M. Kurcbart
  • J. G. Pereira
  • M. A. Manna
Part IV: Two-Dimensional Structures
Part of the Lecture Notes in Physics book series (LNP, volume 393)


We study the surface perturbation of a viscous fluid adequately heated from below. We shown that under appropriate perturbations to the static solution the system exhibit oscillatory instabilities governed by the Kadomtsev-Petviashvili equation or by the (2+1) dimensional Burgers equation.


Solitary Wave Rayleigh Number Viscous Fluid Critical Rayleigh Number Oscillatory Instability 
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  1. 1.
    S. CHANDRASEKHAR, Hydrodynamics and Hydromagnetic Stability (Clarendon, Oxford, 1955).Google Scholar
  2. 2.
    B.B. KADOMTSEV and V.I. PETVIASHVILI, Soviet Physics Dokl. 15, (1970), 539.Google Scholar
  3. 3.
    C.M. ALFARO and M.C. DEPASSIER, Physics Review Letters 62, (1989), 2597.CrossRefGoogle Scholar
  4. 4.
    M. BERTUCCELLI, P. PANTANG and T. BRUGARINO, Lettere Nuovo Cimento, 37, (1987), 433.Google Scholar
  5. 5.
    J.V. WEHAUSEN and E.V. LAITONE in Encyclopaedia of Physics, Vol. 9, Ed. S. Flugge (Springer, Berlin, 1960).Google Scholar
  6. 6.
    G.G. STOKES, Trans. Cambridge Philos. Soc. 8, (1845), 278; reprinted in: Mathematical and Physical Papers. Vol. 1 (Johnson Reprint Corporation, New-York, (1966), 75).Google Scholar
  7. 7.
    S.M. KURCBART, M.A. MANNA, J.G. PEREIRA and A.N. GARAZO, Physical Letters A. 148, (1990), 53.CrossRefGoogle Scholar
  8. 8.
    M. JAULENT, M.A. MANNA and L.M. ALONSO, Inverse Problems 5, (1989) 573.CrossRefGoogle Scholar
  9. 9.
    G.M. WEBB and C.P. ZAUK, Physics Letters A 150, (1990), 14.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • R. A. Kraenkel
    • 1
  • S. M. Kurcbart
    • 1
  • J. G. Pereira
    • 1
  • M. A. Manna
    • 2
  1. 1.Instituto de Física TeóricaUniversidade Estadual PaulistaPaulo, SPBresil
  2. 2.Laboratoire de Physique MathématiqueUniversité MONTPELLIER II, Sciences & Techniques du LanguedocMontpellier CedexFrance

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