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Non-annihilation of travelling pulses in a reaction-diffusion system. (English) Zbl 1166.35342

Summary: 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.

MSC:

35K57 Reaction-diffusion equations
34C99 Qualitative theory for ordinary differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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