COUNTEREXAMPLE TO A CONJECTURE OF GORIELY FOR THE SPEED OF FRONTS OF THE REACTION-DIFFUSION EQUATION

Authors
CISTERNAS J DEPASSIER MC
Citation
J. Cisternas et Mc. Depassier, COUNTEREXAMPLE TO A CONJECTURE OF GORIELY FOR THE SPEED OF FRONTS OF THE REACTION-DIFFUSION EQUATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(3), 1997, pp. 3701-3704
Citations number
12
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
Journal title
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics → ACNP
ISSN journal
1063651X
Volume
55
Issue
3
Year of publication
1997
Part
B
Pages
3701 - 3704
Database
ISI
SICI code
1063-651X(1997)55:3<3701:CTACOG>2.0.ZU;2-G
Abstract
In a recent paper, Goriely [A. Goriely, Phys. Rev. Lett. 75, 2047 (199 5)] considers the one-dimensional scalar reaction-diffusion equation u (t)=u(xx)+f(u), with a polynomial reaction term f(u), and conjectures the existence of a relation between a global resonance of the Hamilton ian system u(xx)+f(u)=0 and the asymptotic speed of propagation of fro nts of the reaction-diffusion equation. Based on this conjecture an ex plicit expression for the speed of the front is given. We give a count erexample to this conjecture and present evidence indicative that it h olds only for a particular class of exactly solvable problems.