Two-dimensional amplitude evolution equations for nonlinear dispersive waves on thin films (Q1115697)

This paper deals with amplitude equations for two-dimensional long waves on the free surface of a thin film flowing down an inclined plane. These equations are generalizations of the result that in the one-dimensional case the Korteweg-de Vries equation applies in a certain limit. Two distinct scalings are considered here and parallel N-soliton solutions are shown to exist in each case. In addition, one of these equations admits two-dimensional solitary waves, but we show that neither equation possesses obliquely-interacting soliton solutions.