Abstract
A nonlinear equation describing the evolution of spatial long-wave perturbations on the surface of a viscous liquid film is considered. The equation is valid for the case of small flow rates and slightly nonlinear perturbations. Steady-state travelling periodic solutions of the equation have been found numerically and analytically. Bifurcation analysis of solutions has been carried out using the methods of stability theory. As a result some new families of spatially periodic solutions have been constructed. Complicated mutual transitions of these families are demonstrated. It is worth to distinguishing the family generating an isolated wave of the horseshoe-like shape in the small wave vector limit.
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