Two-dimensional wave dynamics in thin films. I. Stationary solitary pulses

We consider two-dimensional stationary solitary pulses in a falling film by using the two-dimensional generalized Kuramoto-Sivashinsky equation as a model system. We numerically construct solitary wave solutions of this equation as a function of the dispersion parameter. We obtain an analytical estimate for the speed of these waves in the strongly dispersive case by using a perturbation from the Korteweg-de Vries limit. An impulse response analysis in which the nonlinearity is replaced with a delta function leads to an approximate analytical solution for the shape of two-dimensional solitary waves. The analytical predictions are in excellent agreement with numerical results for the speed and shape of these waves.