Robust balses in reaction-diffusion system

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We have carried out a theoretical analysis and computer simulations on the colision and break-up of pulses in a reaction diffusion system. The collision of pulses can be devided into two categories. One is an elastic-like collision. In this case, two pulses reverse their propagating direction at a finite distance without overlapping. This is called a hard collision. The other is that two pulses overlap each other at a collision, disappear temporally and survive again, which is called a soft collision. The latter is close to the soliton in an integrable system.Our theory of pulse dynamics is successful to clarify the mechanism of the hard collision. That is, the super critical bifurcation from a motionless to a propagating pulse is essential for this phenomenon. Just at postthershold, the velocity of a pulse is so small that the pulse cannot have a sufficient kinetic energy to overcome the potential barriar due to the repulsive nteraction. This fact also explains the reason as to why the elastic-like collision occurs only in a restricted parameter regime in the simulations.The soft collision which is more complicated is left for a future problem. A possible approach is to consider a perturbation of dissipative terms in an integrable limit. A formulation of an interplay between an ossilatory property and an excitable one in the collision process.