Invariant Solutions of the Two-Dimensional Shallow Water Equations with a Particular Class of Bottoms

The two-dimensional shallow water equations with a particular bottom and the Coriolis's force $f=f_{0}+Ωy$ are studied in this paper. The main goal of the paper is to describe all invariant solutions for which the reduced system is a system of ordinary differential equations. For solving the systems of ordinary differential equations we use the sixth-order Runge-Kutta method.

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