Surface perturbations of a shallow viscous fluid heated from below and the (2+1)-dimensional Burgers equation

The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satifies the condition R{≠}30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.