Collision of propagating pulses in a reaction-diffusion system

Recent computer simulations have shown that propagating pulses in a nonlinear dissipative system do not necessarily annihilate upon collision. We address this problem and study the pulse dynamics in a reaction-diffusion system. The equation of motion for a pair of interacting pulses is derived by the interfacial approach. We clarify the condition such that pulses behave as if they are elastic objects. It is emphasized that a supercritically translational bifurcation from a motionless pulse to a propagating pulse plays an important role for the elastic-like collision. Computer simulations of the reaction-diffusion system and the complex Ginzburg-Landau equation are also carried out to confirm our prediction.