The Traveling Wave of Auto-Catalytic Systems-Monotone and Multi-Peak Solutions (Journal of Mathematical Study, 2016)
This article studies propagating wave fronts of a reaction-diffusion system modeling an isothermal chemical reaction $A+2B → 3B$ involving two chemical species,a reactant $A$ and an auto-catalyst $B$, whose diffusion coefficients, $D_A$ and $D_B$, are unequaldue to different molecular weights and/or sizes. Explicit bounds $c_∗$ and $c^∗$ thatdepend on $D_B/D_A$ are derived such that there is a unique travelling wave of everyspeed $c ≥ c^∗$ and there does not exist any travelling wave of speed $c < c_∗$. Furthermore,the reaction-diffusion system of the Gray-Scott model of $A+2B → 3B$, and a lineardecay $B → C$, where $C$ is an inert product is also studied. The existence of multipletraveling waves which have distinctive number of local maxima or peaks is shown. Itshows a new and very distinctive feature of Gray-Scott type of models in generatingrich and structurally different traveling pulses.