  It is well-known that the existence of traveling wave solutions for
reaction-diffusion partial differential equations can be proved by showing the
existence of certain heteroclinic orbits for related autonomous planar
differential equations. We introduce a method for finding explicit upper and
lower bounds of these heteroclinic orbits. In particular, for the classical
Fisher-Kolmogorov equation we give rational upper and lower bounds which allow
to locate these solutions analytically and with very high accuracy.
