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Explicit solutions of Fisher’s equation for a special wave speed. (English) Zbl 0423.35079

35Q99PDE of mathematical physics and other areas
35A05General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI
[1] Ablowitz, M. J., A. Ramani, and H. Segur. 1978. Lettre at Nuovo Cimento, accepted for publication.
[2] Abramowitz, M. and I. Stegun. 1965.Handbook of Mathematical Functions. New York: Dover. · Zbl 0171.38503
[3] Canosa, J. 1969. ”Diffusion in Nonlinear Multiplicative Media.”J. Math. Phys.,10, 1862. · doi:10.1063/1.1664771
[4] Fife, P. C. 1978. ”Asymptotic States for Equations of Reaction and Diffusion.”.Bull Am. Math. Soc.,84, 693--726. · Zbl 0405.35044 · doi:10.1090/S0002-9904-1978-14502-9
[5] Fisher, R. A. 1936. ”The Wave of Advance of an Advantageous Gene.”Ann. Eugen. 7, 355--369. · doi:10.1111/j.1469-1809.1937.tb02153.x
[6] Hoppensteadt, F. C. 1975.Mathematical Theories of Populations: Demographics, Genetics and Epidemics. CMBS Vol. 20, Philadelphia: SIAM Publication. · Zbl 0304.92012
[7] Ince, E. I. 1956.Ordinary Differential Equations. New York: Dover. · Zbl 0063.02971
[8] Kolmogorov, A., I. Petrovskii and N. Piskunov 1937. ”Étude de l’Équation de la Diffusion avec Croissance de la Quantité de la Matière et Son Application à un Problème Biologique.”Moscow Univ. Bull. Math.,1, 1--25.
[9] Lefschetz, S. 1963:Differential Equations: Geometric Theory, 2nd ed., pp. 95--111. New York: Interscience. · Zbl 0107.07101
[10] McKean, H. P.. 1975. ”Application of Brownian Motion to the Equation of Kolmogorov-Petrovskii-Piskunov.”Communs Pure appl. Math. 28, 323--331. · Zbl 0316.35053 · doi:10.1002/cpa.3160280302
[11] Zeppetella, A. and M. J. Ablowitz. 1978. ”On Solutions of Some Nonlinear Ordinary Differential Equations with Applications to Fisher’s Equations.” To be submitted toSIAM J. Appl. Math.