TY - JOUR

T1 - Counterexample to a conjecture of Goriely for the speed of fronts of the reaction-diffusion equation

AU - Cisternas, J.

AU - Depassier, M. C.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevE.55.3701

DO - 10.1103/PhysRevE.55.3701

M3 - Article

VL - 55

SP - 3701

EP - 3704

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

ER -