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Some families of exact solutions of the equations of two-dimensional shallow water theory

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Abstract

Results are presented of a study of the exact solutions of the equations of two-dimensional unsteady and steady shallow water theory, based on the group properties of these equations. The first part presents the group properties of the equations in question; the second part presents the invariant solutions of these equations.

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Authors and Affiliations

  1. Novosibirsk

    M. T. Gladyshev

Authors
  1. M. T. Gladyshev
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 6, pp. 62–71, November–December, 1969.

The author wishes to thank L. V. Ovsyannikov and N. Kh. Ibragimov for valuable guidance in carrying out this study.

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Gladyshev, M.T. Some families of exact solutions of the equations of two-dimensional shallow water theory. J Appl Mech Tech Phys 10, 896–905 (1969). https://doi.org/10.1007/BF00907924

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  • DOI: https://doi.org/10.1007/BF00907924

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