Entire solutions in monostable reaction–advection–diffusion equations in infinite cylinders

This paper is concerned with entire solutions of a monostable reaction–advection–diffusion equation in infinite cylinders without the condition f′(u)≤f′(0)f′(u)≤f′(0). By constructing a quasi-invariant manifold, we prove that there exist two classes of entire solutions. Furthermore, we show that one class of such entire solutions is unique up to space and time translation.