Propagation equations for waves in moving thin films of perfect liquids with weak sources at the bottom

Abstract

The paper deals with the problem of modelling nonlinear waves propagation in thin liquid layers in the presence of weak sources at the bottom. It is established the conditions under which the model equation has the left-hand side bearing a resemblance to the Korteweg-de-Vries equation with slowly evolved parameters, and perturbed right-hand side. At the same time the specific conditions under which the appearance of solitary waves can be nevertheless possible have been defined.