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The paper deals with the canard traveling waves in a reaction–diffusion model. The use of the geometric theory of invariant manifolds allows us to simplify the traveling wave problem of the original PDE system. We are focused on point-to-periodic traveling waves. It is shown that the profile of such waves is a canard. Canard traveling waves are critical waves since they separate waves with qualitatively different behaviors.

The paper deals with a special type of traveling waves in a combustion model. A non–adiabatic case of autocatalytic combustion reaction in one spatial dimension is considered. The existence of critical traveling waves is stated. The critical traveling waves play the role of an intermediate form, they separate the waves of slow burnout and waves corresponding to the thermal explosion. It is shown that the profiles of the critical waves are canards. An asymptotic representation for the speed of the critical traveling wave is obtained.