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On the theory of acoustic solitons in a liquid with distributed gas bubbles

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Abstract

A close relation is established between numerical solutions to two systems of equations, viz., the two-level nonlinear wave dynamic model of a liquid with gas bubbles and the Korteweg-de Vries (KdV) equation. This model is used for deriving the KdV equation in the long-wave approximation for any dependent variable of the gas-liquid mixture. The KdV equations derived earlier using radically different approximations are particular cases of our equations.

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References

  1. R. K. Dodd, J. C. Eilbeck, J. D. Gibbson, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1982; Mir, Moscow, 1988).

    MATH  Google Scholar 

  2. Yu. S. Kivshar and G. P. Agraval, Optical Solitons: From Fibers to Photonic Crystals (Academic, Amsterdam, 2003; Fizmatlit, Moscow, 2005).

    Google Scholar 

  3. K. Naugolnykh and L. Ostrovsky, Nonlinear Wave Processes in Acoustics (Cambridge Univ., Cambridge, 1998).

    MATH  Google Scholar 

  4. L. Van Wijngaarden, J. Fluid Mech. 33, 465 (1968).

    Article  MATH  ADS  Google Scholar 

  5. V. E. Nakoryakov, V. V. Sobolev, and I. R. Shreiber, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 71 (1972).

  6. V. N. Alekseev and S. A. Rybak, Akust. Zh. 41, 690 (1995) [Acoust. Phys. 41, 607 (1995)].

    Google Scholar 

  7. E. A. Zabolotskaya, Akust. Zh. 21, 934 (1975) [Sov. Phys. Acoust. 21, 569 (1975)].

    Google Scholar 

  8. D. Ch. Kim, Pis’ma Zh. Tekh. Fiz. 32(5), 38 (2006) [Tech. Phys. Lett. 32, 204 (2006)].

    Google Scholar 

  9. D. C. Kim, Comp. Phys. Commun. 147, 526 (2002).

    Article  MATH  ADS  Google Scholar 

  10. D. G. Crighton and J. E. Williams, J. Fluid Mech. 36, 585 (1969).

    Article  MATH  ADS  Google Scholar 

  11. O. V. Rudenko, Usp. Fiz. Nauk 176, 77 (2006) [Phys. Usp. 49, 69 (2006)].

    Article  Google Scholar 

  12. N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett. 15, 240 (1965).

    Article  ADS  Google Scholar 

  13. Yu. F. Berezin and V. I. Karpman, Zh. Éksp. Teor. Fiz. 51, 1551 (1966) [Sov. Phys. JETP 24, 1049 (1966)].

    Google Scholar 

  14. V. E. Zakharov and L. D. Faddeev, Funct. Anal. Appl. 5(4), 18 (1971).

    Google Scholar 

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Authors and Affiliations

  1. Siberian State University of Telecommunication and Information Sciences, Novosibirsk, 630102, Russia

    D. Ch. Kim

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  1. D. Ch. Kim
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Original Russian Text © D.Ch. Kim, 2007, published in Zhurnal Tekhnicheskoĭ Fiziki, 2007, Vol. 77, No. 6, pp. 8–12.

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Kim, D.C. On the theory of acoustic solitons in a liquid with distributed gas bubbles. Tech. Phys. 52, 685–689 (2007). https://doi.org/10.1134/S1063784207060023

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  • DOI: https://doi.org/10.1134/S1063784207060023

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