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Solutions of shallow-water equations in non-rectangular cross-section channels. (English) Zbl 1154.76012

Summary: We study smooth solutions of the shallow-water equations for non-rectangular cross-section channels. It is found that a complete set of solutions can be classified in four Lie symmetry groups that show distinctive physical features.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
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