Stability of front solutions in a model for a surfactant driven flow on an inclined plane

• We study fronts in a model for a flow of a thin liquid film down an inclined plane.
• In a system without a surfactant, the front has no unstable spectrum.
• With a surfactant, there are regimes when the front has no unstable spectrum.
• The results are based on analytical and numerical methods.

We consider a model for the flow of a thin liquid film down an inclined plane in the presence of a surfactant. The model is known to possess various families of traveling wave solutions. We use a combination of analytical and numerical methods to study the stability of the traveling waves. We show that for at least some of these waves the spectra of the linearization of the system about them are within the closed left-half complex plane.