  Several new families of nonlinear three-dimensional travelling wave solutions
to the Navier-Stokes equation, also known as exact coherent states, are
computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex
structures are reported and their possible connections to critical layer
dynamics examined. While some of the solutions clearly display fluctuations
that are localized around the critical layer (the surface on which the
streamwise velocity matches the wave speed of the solution), for others this
connection is not as clear. Dynamical trajectories along unstable directions of
the solutions are computed. Over certain ranges of Reynolds number, two
solution families are shown to lie on the basin boundary between laminar and
turbulent flow. Direct comparison of nonlinear travelling wave solutions to
turbulent flow in the same channel is presented. The state-space dynamics of
the turbulent flow are organized around one of the newly-identified travelling
wave families, and in particular the lower branch solutions of this family are
closely approached during transient excursions away from the dominant
behaviour. These observations provide a firm dynamical-systems foundation for
prior observations that minimal channel turbulence displays time intervals of
"active" turbulence punctuated by brief periods of "hibernation" (see e.g. Xi,
L. and Graham, M. D., Phys. Rev. Lett., 104, 218301 (2010)). The hibernating
intervals are approaches to lower branch nonlinear travelling waves.
Representing these solutions on a Prandtl-von Karman plot illustrates how their
bulk flow properties are related to those of Newtonian turbulence as well as
the universal asymptotic state called maximum drag reduction (MDR) found in
viscoelastic turbulent flow.
