(A) A typical plot of Re[λmax(V)], the maximum growth rate of perturbations to the wavetrain in a frame of reference moving with velocity V (ω1 = 2,c inv = 2). (B) Plots of V L, V R, and V band vs ω1. The wavetrain becomes unstable at ω1 = ω1 stab; here V L = V R = V band. As ω1 is increased, the range of frame velocities for which the wavetrain is unstable grows, and V band increases. At ω1 = ω1 max, the V band curve folds, at V band = V R = 2, which is the invasion speed c inv. The “kink” that is visible in the V L curve at ω1 = 2.20 corresponds to a triple point (see Methods). For ω1 > 2.2, νmax(V L) has a nonzero imaginary part, whereas for ω1 < 2.2 it is real.