Multiple-peak traveling waves of the Gray-Scott model

We study a reaction-diffusion system which models the pre-mixed isothermal autocatalytic chemical reaction of order m (m > 1) between two species, reactant A and an auto-catalyst B, + B --> (m+1) linear decay -->C, where C is inert product. The special case = 2 much studied Gray-Scott model, but without feeding. prove existence multiple traveling waves have distinctive number local maximaor peaks. It shows new very feature type in generating rich structurally different pulses than related literature such as autocatalysis decay, or bio-reactor model with 1 m-th decay.