  The forced Korteweg-de Vries (fKdV) equation describes incompressible
inviscid free surface flows over some arbitrary topography. We investigate
solitary and hydraulic fall solutions to the fKdV equation. Numerical results
show that the calculation of exponentially decaying solitary waves at the
critical Froude number is a nonlinear eigenvalue problem. Furthermore we show
how exponential decaying solitary waves evolve into the continuous spectrum of
algebraic decaying solitary waves. A novel and stable numerical approach using
the wave-resistance coefficient and tabletop solutions is used to generate the
hydraulic fall parametric space. We show how hydraulic fall solutions
periodically evolve into exponential decaying solitary waves.
