Counterexample to a conjecture of Goriely for the speed of fronts of the reaction-diffusion equation

In a recent paper, Goriely [A. Goriely, Phys. Rev. Lett. 75, 2047 (1995)] considers the one-dimensional scalar reaction-diffusion equation [formula presented]=[formula presented]+f(u), with a polynomial reaction term f(u), and conjectures the existence of a relation between a global resonance of the Hamiltonian system [formula presented]+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 present evidence indicative that it holds only for a particular class of exactly solvable problems.