Fisher-KPP Traveling Wave

The Fisher-KPP equation ∂u/∂t = D∂²u/∂x² + ru(1−u) admits traveling wave solutions. The minimum selected speed is c* = 2√(rD). Steep initial conditions select c*, while shallow conditions can select faster (pushed) fronts.

Selected speed:
c* = 2√(rD)

Pulled front: steep IC → c*
Pushed front: shallow IC → c > c* possible with nonlinear diffusion

Profile: u ≈ (1+Ae^{λx})^{-2}
λ = c/(2D) − √(c²/4D² − r/D)
c_measured = —