Analytical Techniques for the Problem of the Interaction of Nonlinear Sonic Waves with Nonuniform Media

  • A. A. Lugovtsov
Conference paper


Equations describing the propagation of waves with small but finite amplitude in the presence of bubbles with different radii are deduced, keeping account of the dependence of their distribution on space coordinates. The laws of conservation are shown to be significant in choosing the solutions coincident in basic physical properties with the solutions of the initial system. In some particular cases, the equations thus deduced are such known equation as KDV, Kadomtsev-Petviashvily and Khokhlov-Zabolotskaya.

Key words

Nonlinear waves Nonuniform media 


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  1. Gavrilyuk SL (1991) Preprint Nl, Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, NovosibirskGoogle Scholar
  2. Lugovtsov AA (1991) Dinamika Sploshnoy Sredy 100:148 (Institute of Hydrodynamics, Novosibirsk).MathSciNetGoogle Scholar
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  4. Lugovtsov AA (1980) Jurnal Prikladnoy Mechaniki i Technicheskoy Fiziki (PMTF) 6: 24MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • A. A. Lugovtsov
    • 1
  1. 1.Institute of Thermophysics, Siberian Branch of Russian Academy of SciencesNovosibirskRussia

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