The Perturbative and Poincare Stability of the Travelling Wave Solution of the Logistic Growth with Non-Linear Advection

We obtain a new proof for the perturbative stability of a travelling wave solution of the logistic growth model with a simple non-linear advection. We also show that a solution with a negative velocity near its zero critical point is stable, whereas a solution near the other critical point is stable if only the coordinate velocity of the wave is greater than the product of the limit of the logistic curve and the parameter of the advection term.