Journal of Applied Mechanics and Technical Physics

, Volume 49, Issue 5, pp 737–748 | Cite as

Symmetries and exact solutions of the shallow water equations for a two-dimensional shear flow



This paper considers nonlinear equations describing the propagation of long waves in two-dimensional shear flow of a heavy ideal incompressible fluid with a free boundary. A nine-dimensional group of transformations admitted by the equations of motion is found by symmetry methods. Two-dimensional subgroups are used to find simpler integrodifferential submodels which define classes of exact solutions, some of which are integrated. New steady-state and unsteady rotationally symmetric solutions with a nontrivial velocity distribution along the depth are obtained.

Key words

symmetry exact solutions two-dimensional shear flows long waves 


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Copyright information

© MAIK/Nauka 2008

Authors and Affiliations

  1. 1.Lavrent’ev Institute of Hydrodynamics, Siberian DivisionRussian Academy of SciencesNovosibirskRussia

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