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

J. Cisternas, M. C. Depassier

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.
Original languageAmerican English
Pages (from-to)3701-3704
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume55
Issue number3
DOIs
StatePublished - 1 Jan 1997
Externally publishedYes

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