Dissipative Korteweg–de Vries description of Marangoni–Bénard oscillatory convection

For a horizontal liquid layer open to air and heated either from the air side or the liquid side, threshold values for the onset of oscillatory interfacial instability are provided, as well as the nonlinear evolution equation describing the deformable open surface. The latter equation is the dissipation-modified Korteweg–de Vries evolution equation for solitary excitations in the liquid layer.