Figure 5

Example of a plot of $Re(\rho )$ along the real axis for the two species example illustrated in Figures 3 and 4 ($f_1=0.3$, $f_2=0.7$, $A_1=1$ and $A_2=2$) with $v_p=1.54$. Poles of $Re(\rho )$ are indicated with dashed grey lines and occur at $-A_1$, $-A_2$ (both poles of g) and ${\lambda }_1$ (zero of g). The minimum at ${\lambda }_{\ast }$ (solid grey line) is a saddle point in the complex λ plane through which we must deform the integration contour when applying the method of steepest descents (see Figure 6).