Dispersion-modified burgers description for nonlinear surface wave excitations in Benard-Marangoni convection

The evolution of long nonlinear surface wave excitations in a Benard-Marang oni shallow liquid layer is studied when the system is far from its instabi lity threshold. For(M - M-c)/M-c = O(1), thus for surface wave excitations with possible large amplitude, where M is the Marangoni number of the syste m and M-c is its critical value bifurcating to oscillatory convecting state from a motionless one, the surface wave displacement is found to obey a di spersion-modified Burgers equation whose kink-like solutions are also studi ed.