Given Fisher's equations: \begin{align*} \frac{\mathrm dP}{\mathrm dz}&=S,\\ \frac{\mathrm dS}{\mathrm dz}&=-\frac{\alpha}{D}P(1-P)-\frac{v}{D}S. \end{align*}
How would you estimate the minimum wave speed?
I have performed stability analyses on these two equations and I concluded that steady state $(P,S) = (0,0)$ would be a stable node and $(1,0)$ must be a saddle in order to give rise to a traveling wave.
I'm not entirely sure how to approach the minimum wave speed from here. Do I take the derivative in terms of $v$ somehow in the second equation?
Any insights would be appreciated!