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

Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations