  New equilibrium solution branches for plane Couette flow are reported which
add to the inventory of known solution branches. The exact solutions are found
by projecting known equilibria onto the resolvent modes of McKeon & Sharma (J.
Fl. Mech., vol. 658, 2010, pp. 336-382) to generate approximate solutions that
are subsequently used as seeds in a Newton-Krylov-hookstep search. Searches
initialised with these projections have a convergence rate of 96%, leading to
the discovery of 16 new equilibria. The low-dimensional nature of the resulting
equilibria is attributed to the projection generated by the resolvent model;
resolvent modes for a given equilibrium solution span a low-dimensional space
which the solution approximately inhabits. This property is exploited to
generate new branches of equilibria in plane Couette flow, and to jump to known
branches. The new branches include bifurcations from previously known
bifurcation curves and a disconnected bifurcation curve which displays
interesting behaviour when continued in Reynolds number. The unstable manifolds
of the new exact coherent states are also computed to expand the known state
space structure of plane Couette flow.
