I don't know how to to do this one part of a problem from my (non-PDE) math course. It's about the Fisher's equation. I've never encountered it before.
$$\frac{\partial P}{\partial t} = D \frac{\partial^2 p}{\partial x^2} + ap(1-p) $$
How do I (1) show that the travelling wave solutions to this ($S(z)=p(x,t)$, where $z=x-vt$) must satisfy:
$$\frac{dP}{dz} = S$$ $$\frac{dS}{dz} = -\frac{a}{D} P(1-P) - \frac{v}{D}S$$
and (2) deduce the minimum travelling speed.
Thanks.