Fronts and pulses near plane Kolmogorov flow and bifurcation without prameters

We consider the Kolmogorov problem of viscous incompressible planar fluid flow under external spatially periodic forcing. Looking for time-independent bounded solutions near the critical Reynolds number, we use the Kirchgässner reduction to obtain a spatial dynamical system on a 6-dimensional center manifold. The dynamics is generated by translations in the unbounded spatial direction. Reduction by first integrals yields a 3-dimensional reversible system with a line of equilibria. This line of equilibria is neither induced by symmetries, or by first integrals. At isolated points, normal hyperbolicity of the line fails due to a transverse double eigenvalue zero. In particular we describe the complete set of all small bounded solutions. In the classical Kolmogorov case, consists of periodic profiles, homoclinic pulses and a heteroclinic front-back pair. This is a consequence of the symmetry of the external force.