Figure 2
From: Modulation Instability and Phase-Shifted Fermi-Pasta-Ulam Recurrence

Trajectories (bold circles) in the complex plane describing the MI with the highest initial growth rate.
The circle around the origin (dashed curve) is the manifold of initial conditions. Here κ = 1, i.e. a1 = 1/4. The dotted lines schematically show two qualitatively different types of periodic solution close to the separatrix. The curves labeled A correspond to solution (2), while curve B corresponds to (6).