Exact solutions in front propagation problems with superdiffusion

Front propagation in a number of reaction–superdiffusion problems is studied. Specifically, traveling wave propagation, domain wall pinning, and systems of waves governed by a bistable single equation as well as FitzHugh–Nagumo equations are considered. The reaction terms in the equations are taken in the form of piecewise linear functions, which allow for exact solutions to be obtained. The effect of superdiffusion on front propagation is discussed.