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December 2002 Non-annihilation of Travelling Pulses in a Reaction-diffusion System
M. Mimura, M. Nagayama, T. Ohta
Methods Appl. Anal. 9(4): 493-516 (December 2002).


It is demonstrated that slowly travelling pulses arising in a reaction-diffusion (RD) system with the FitzHugh-Nagumo type nonlinearity do not necessarily annihilate but reflect off of each other before they collide. This phenomenon is in contrast with the well-known annihilation of travelling pulses on nerve axon and expanding rings in the Belousov-Zhabotinsky chemical reaction. By using singular perturbation methods, we derive a fourth order system of ODEs from the RD system, and study non-annihilation phenomenon of very slowly travelling pulses.


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M. Mimura. M. Nagayama. T. Ohta. "Non-annihilation of Travelling Pulses in a Reaction-diffusion System." Methods Appl. Anal. 9 (4) 493 - 516, December 2002.


Published: December 2002
First available in Project Euclid: 1 September 2009

zbMATH: 1166.35342
MathSciNet: MR2006602

Rights: Copyright © 2002 International Press of Boston


Vol.9 • No. 4 • December 2002
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