Comments on the paper “Chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow”

In the commented paper the authors consider a model of a two-dimensional airfoil with cubic nonlinearity in supersonic flow. They claim to prove the existence of Siʼlnikov homoclinic orbits by using the undetermined coefficient method and, consequently, Smale horseshoe chaos occurs via Siʼlnikov criterion. Unfortunately, their demonstration is invalid because the form of the function they assume in the series expansion for the homoclinic orbits is incorrect. Namely, they compose the homoclinic orbit of the same manifold, which is stable in forward time and unstable in reverse time.