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Soliton propagation in a wide channel with an uneven bottom

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Abstract

Nonlinear waves of small amplitude in wide horizontal channels are considered. The channel depth is assumed to be a function weakly dependent on the transverse coordinate. To describe the waves, the two-dimensional Boussinesq equations in the form obtained in this paper are used. Stationary solutions in the form of a soliton followed by a set of sinusoidal waves are found. The phase velocity of these waves in the channel direction is equal to the soliton velocity.

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References

  1. G. B. Witham,Linear and Nonlinear Waves, Wiley, New York (1974).

    Google Scholar 

  2. J. Lighthill,Waves in Fluids, University Press, Cambridge (1978).

    MATH  Google Scholar 

  3. D. H. Peregrine, "Long waves on a beach," J. Fluid Mech.,27, 815–827 (1967).

    Article  MATH  ADS  Google Scholar 

  4. E. I. Bichenkov and R. M. Garipov, "Propagation of waves on the surface of a heavy fluid in a basin with an uneven bottom,"Zh. Prikl. Mat. Tekhn. Fiz., no. 2, 21–26 (1969).

    Google Scholar 

  5. A. G. Kulikovskii and V. A. Reutov, "Propagation of nonlinear waves over semi-infinite underwater trenches and ridges,"Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, no. 2, 53–61 (1980).

  6. I. B. Bakholdin, "Discontinuities of the variables characterizing solitary wave propagation in a fluid layer,"Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, no. 3, 87–93 (1984).

  7. C. C. Mei,The Applied Dynamics of Ocean Surface Waves, World Scientific, Singapore (1989).

    MATH  Google Scholar 

  8. C. C. Mei and B. Le Méhaute, "Note on the equations of long waves over an uneven bottom," J. Geophys. Res.,71, 393–400 (1966).

    ADS  Google Scholar 

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Authors
  1. Yu. A. Drozdova
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Additional information

Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 147–155, July–August, 2000.

The work was financially supported by the Russian Foundation for Basic Research (project No. 99-01-00277).

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Drozdova, Y.A. Soliton propagation in a wide channel with an uneven bottom. Fluid Dyn 35, 591–598 (2000). https://doi.org/10.1007/BF02698129

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  • DOI: https://doi.org/10.1007/BF02698129

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