  The finite element method is applied to obtain numerical solutions to the
recently derived nonlinear equation for shallow water wave problem for several
cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal
waves under stochastic forces are presented. Though small effects originating
from second order dynamics may be obscured by stochastic forces, the main
waves, both cnoidal and solitary ones, remain very robust against any
distortions.
