This model was originally proposed by Exner (1925). Assuming a smooth initial condition,
z ( x, 0) = z0 , the classical solution is given implicitly by:
(ζ - z )
z ( x, t ) = z0 ( x - czt ) ,
2
cz = Aq f
(11)
where cz is the propagation speed of the bed. As is well known, non-linear hyperbolic equations