Abstract
We classify all possible algebraic traveling solutions for the family of second order reaction-diffusion equations
where f is a polynomial function and \(d>0\) and r are real constants. In particular, we provide all the algebraic traveling wave solutions of the celebrated Nagumo equation.
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References
Ablowitz, M.J., Segur, H.: Solitons and Inverse Scattering Transform. SIAM, Philadelphia (1981)
Bleecker, D., Csordas, G.: Basic Partial Differential Equations. Van Nostrand Reinhold, New York (1992)
Britton, N.F.: Reaction-Diffusion Equations and Their Applications to Biology. Academic Press, London (1986)
Fisher, R.A.: The wave of advance of advantageous genes. Ann. Eugen. 7, 355–369 (1937)
Gasull, A., Giacomini, H.: Explicit travelling waves and invariant algebraic curves. Nonlinerity 28, 1597–1606 (2015)
Hayashi, M.: On polynomial Liénard systems which have invariant algebraic curves. Funkc. Ekvacioj 39, 403–408 (1996)
Liu, G.T., Fan, T.Y.: New applications of developed Jacobi elliptic function expansion methods. Phys. Lett. A 345, 161–166 (2005)
Murray, J.D.: Mathematical biology. I. An introduction, 3rd edn. In: Antman, S.S., Marsden, J.E., Sirovich, L., Wiggins, S. (eds.) Interdisciplinary Applied Mathematics, p 17. Springer, New York (2002)
Newell, A.C., Whitehead, J.A.: Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279–303 (1969)
Wang, M.L.: Exact solutios for a compound KdV Burgers equation. Phys. Lett. A 213, 279–287 (1996)
Zeldovich, Y.B., Frank-Kamenetskii, D.A.: A theory of thermal propagation of flames. Acta Physicochim. USSR 9, 341–350 (1938)
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Valls, C. Algebraic traveling waves for some family of reaction-diffusion equations including the Nagumo equations. Nonlinear Differ. Equ. Appl. 24, 25 (2017). https://doi.org/10.1007/s00030-017-0450-1
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DOI: https://doi.org/10.1007/s00030-017-0450-1