Lie Symmetry Analysis of the One-Dimensional Saint-Venant-Exner Model

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