Speed of Fronts of the Reaction-Diffusion Equation.

In a recent paper Goriely considers the one–dimensional scalar reaction– diffusion equation ut = uxx + f(u) with a polynomial reaction term f(u) and conjectures the existence of a relation between a global resonance of the hamiltonian system uxx+f(u) = 0 and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold. 82.40.Ck, 47.10+g, 3.40Kf, 2.30.Hq Typeset using REVTEX 1