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2003 | 103 | 4 | 365-371
Article title

Stability of Deep Water Waves Governed by the Benjamin-Ono Equation

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EN
Abstracts
EN
The Benjamin-Ono equation models the dynamics of internal waves in stratified fluids of great depth. It includes an integral (Hilbert transform) term, and so stability calculations might seem difficult. We expand in both the amplitude of the nonlinear wave and the wave vector of the perturbation, assumed to be small quantities of the same order. An expression for the nonlinear dispersion relation is obtained. Nonlinear periodic Benjamin-Ono waves are stable, just as the localized, algebraic soliton solutions (Lorentzians), already known to be stable. (This also follows as a limit of our calculations.) We extend the known analogy between the Benjamin-Ono and modified Korteweg-de Vries equations.
Keywords
EN
Contributors
author
  • Sołtan Institute for Nuclear Studies, Hoża 69, 00-681 Warsaw, Poland
author
  • Department of Physics, University of Warwick, Coventry CV4 7AL, UK
References
  • 1. T.E. Benjamin, J. Fluid Mech., 29, 559, 1967; R.A. Davis, A. Acrivos, J. Fluid Mech., 29, 593, 1967
  • 2. H. Ono, J. Phys. Soc. Jpn., 39, 1082, 1975
  • 3. B. Fuchssteiner, T. Schultze, Phys. Lett. A, 204, 336, 1995
  • 4. K.M.T. Tamizhmani, A. Ramani, B.J. Grammaticos, J. Phys. A, 30, 1017, 1997
  • 5. Y.J. Matsumo, J. Phys. A, 12, 125, 1979
  • 6. Y.J. Matsumo, Phys. Soc. Jpn., 57, 1924, 1988
  • 7. T. Miloh, M. Prestin, L. Shtilman, M.P. Tulin, Wave Motion, 17, 11, 1993
  • 8. Y. Matsumo, D.J. Kaup, J. Math. Phys., 38, 5195, 1997
  • 9. D.J. Kaup, T.I. Lakoba, Y. Matsumo, Inverse Problems, 15, 215, 1999
  • 10. B. Fornberg, G.B. Whitham, Philos. Trans. R. Soc. Lond. A, 289, 373, 1978
  • 11. K. Murawski, E. Infeld, Aust. J. Phys., 41, 1, 1988
  • 12. E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos, 2nd ed., Cambridge University Press, Cambridge, UK 2000, Chapter 5; E. Infeld, G. Rowlands, A. Senatorski, Proc. R. Soc. Lond. A, 455, 4363, 1999; E. Infeld, A.A. Skorupski, G. Rowlands, ibid., 458, 1231, 2002
  • 13. G.B. Whitham, Linear and Nonlinear Waves, Wiley, New York 1974
  • 14. T.L. Perelman, A.K. Friedman, M.M. Elyashvich, Phys. Lett. A, 47, 321, 1974
  • 15. E.J. Hanamura, Phys. Soc. Jpn., 37, 1598, 1974
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv103n406kz
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