Formation of patterns induced by thermocapillarity and gravity

Consider a liquid film on a slightly inclined plane driven by gravity and thermocapillarity. We derive an equation describing the nonlinear evolution of the interface between the liquid and the atmosphere. In line with an approach introduced by us elsewhere we preserve the full impact of the curvature that contributes toward formation of bubbles and together with convection induced by the inclined plane contributes toward either breaking of waves or prevention of rupture that otherwise will always occur. Travelling waves are also possible. A variety of possible equilibrium states is also discussed.