Abstract
We present the Lie symmetry analysis for a hyperbolic partial differential system known as the one-dimensional Saint-Venant-Exner model. The model describes shallow-water systems with bed evolution given by the Exner terms. The sediment flux is considered to be a power-law function of the velocity of the fluid. The admitted Lie symmetries are classified according to the power index of the sediment flux. Furthermore, the one-dimensional optimal system is determined in all cases. From the Lie symmetries we derive similarity transformations which are applied to reduce the hyperbolic system into a set of ordinary differential equations. Closed-form exact solutions, which have not been presented before in the literature, are presented. Finally, the initial value problem for the similarity solutions is discussed.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)