Fisher-KPP equation Can you help me understand how to derive the Fisher-KPP equation? I.e., how can I figure out where it comes from? 
It is easy to find the derivations of the diffusion equation and the heat equation, but I can't find any summary of the way to derive this one...
Will you please help me?
Thanks
 A: I am giving you a rather more intuitive argument here: for equation
$$ \frac{\partial u}{\partial t}=r u(1-u)+\color{blue}{\frac{\partial^2 u}{\partial x^2}},\tag{1}$$ 
if we ignore the blue term, it is just:
$$
\frac{\partial u}{\partial t}=ru(1-u),\tag{2}
$$
which is a Logistic equation. Above pure Logistic equation models the change of a population having growth rate $r$. With blue term added, it means a diffusion is added spacially, which can be interpreted as: a bump somewhere in the quantity $u$ will propagate in space, in this case, in a nonlinear way like Burgers' equation.
The equilibria and their stability of (1) inherit the ones in (2), which are $u\equiv 1$ (stable) and $u\equiv 0$ (unstable). The traveling wave solution physically describes an traveling wavefront from the region near the stable solution $u=1$ to the region near unstable solution $u=0$.
Also judging by the first few pages of the paper A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem by Kolmogorov-Petrovskii-Piscounov (my library doesn't have this article), the notation is more user-friendly and you might wanna check that out.
