On nontrivial traveling waves in thin film flows including contact lines

We discuss dynamics of thin liquid films spreading down an inclined plane. The fronts of these films are known to be unstable with respect to formation of finger-like and triangular patterns. In this work, we concentrate on one particular aspect of these flows, and that is the existence of nonlinear traveling waves. We find evidence for presence of these waves for all inclination angles less than 90°. To understand better the relevant pattern formation mechanism, we explore via numerical simulations the bifurcation structure of the stability diagram close to the critical wavenumber. The recovered structure is consistent with the existence of a subcritical bifurcation. We discuss the connection between the bifurcation diagram and the existence of nontrivial traveling waves.