Order reduction for critical traveling wave problems

The paper deals with the order reduction for critical traveling wave problems. The specificity of such traveling waves is that they separate waves with qualitatively different behaviors. W e show how the application of the geometric theory of singular perturbations allows us to reduce the traveling wave problem for the original PDE system to the analysis the projection of the system onto its slow invariant manifold. W e illustrate this approach to the problem of finding the point-to-periodic traveling wave for the reaction-diffusion model. (paper)