Numerical solution of a KdV equation, model of a free surface flow

A KdV equation is considered as a model of free surface flow disturbed by a bump. The equation has a parameter related to the Froude number, defined as the upstream flow, and it has a forcing term as representation of the bottom topography. From the analytical solution, that can be obtained for special case of the bottom topography, i.e when it is a solitary form of secant hyperbolic function, a numerical method is developed to confirm that solution. The method is based on a finite difference. As the result, our numerical procedure gives two solutions. Only one agrees with the analytical solution, but it does not confirm to the limiting case of the solution obtained from unsteady problem, the second solution does.