Speed shift in reaction–diffusion equations with cutoff

Front solutions in a reaction–diffusion equations with cutoff are obtained analytically using piecewise linear approximations of the reaction term. The piecewise emulation allows us to study analytically the effect of the cutoff for fronts propagating into metastable and unstable states. A general relationship between the cutoff threshold and the parameters involved into the reaction term is derived. Our results are in excellent agreement with that existing in the literature and prove that the piecewise emulation is an useful procedure to deal with complex reaction–diffusion equations under cutoff.