Mimura, M.; Nagayama, M.; Ohta, T. Non-annihilation of travelling pulses in a reaction-diffusion system. (English) Zbl 1166.35342 Methods Appl. Anal. 9, No. 4, 493-515 (2002). 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. Cited in 4 Documents 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 × Cite Format Result Cite Review PDF Full Text: DOI