Snakes and ladders: localized solutions of plane Couette flow.

We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in one spatial dimension. Solutions of different size are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. These new solutions are a step towards extending the dynamical systems view of transitional turbulence to spatially extended flows.