  We study a simple two-dimensional model for motion of an elastic filament
subject to internally generated stresses and show that wave-like propagating
shapes which can propel the filament can be induced by a self-organized
mechanism via a dynamic instability. The resulting patterns of motion do not
depend on the microscopic mechanism of the instability but only of the filament
rigidity and hydrodynamic friction. Our results suggest that simplified
systems, consisting only of molecular motors and filaments could be able to
show beating motion and self-propulsion.
