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

New equilibrium solution branches of plane Couette flow discovered using a project-then-search method