Existence of the Kink Wave Solutions of the Porous–Fisher–KPP Equation

In this paper, we prove the existence of the kink wave solutions of the Porous–Fisher–KPP equation. With the method of dynamical systems, we find bifurcations in the phase portraits for the corresponding traveling wave dynamical system under given parameter conditions. By using the property of the generalized one-parameter family of rotated vector fields with respect to a key parameter on the right-hand phase plane, we establish the existence of connecting orbits for the corresponding traveling system.