Kudryashov, N. A.; Zakharchenko, A. S. A note on solutions of the generalized Fisher equation. (English) Zbl 1327.35165 Appl. Math. Lett. 32, 53-56 (2014). Summary: The generalized Fisher equation is considered. Possible exact solutions of this equation are found by \(Q\)-function method. The velocities of traveling waves are determined and analyzed. Cited in 24 Documents MSC: 35K55 Nonlinear parabolic equations 35C05 Solutions to PDEs in closed form 35C07 Traveling wave solutions Keywords:nonlinear differential equation; Fisher equation; exact solution; \(Q\)-function method PDF BibTeX XML Cite \textit{N. A. Kudryashov} and \textit{A. S. Zakharchenko}, Appl. Math. Lett. 32, 53--56 (2014; Zbl 1327.35165) Full Text: DOI References: [1] Fisher, R. A., The wave of advance of advantageous genes, Ann. Eugenics, 7, 335-369, (1937) · JFM 63.1111.04 [2] Kolmogorov, A. N.; Petrovsky, I. G.; Piscunov, N. S., Investigation of a diffusion equation connected to the growth of materials, and application to a problem in biology, Bull. Univ. Moscow, Ser. Int. Sec. A, 1, 1-26, (1937), (in Russian) [3] Ablowitz Mark, J.; Zeppetella, Anthony, Explicit solutions of fisher’s equation for a special wave speed, Bull. Math. Biol., 41, 6, 835-840, (1979) · Zbl 0423.35079 [4] Korpusov, M. O.; Ovchinnikov, A. V.; Sveshnikov, A. G., On blow up of generalized Kolmogorov-Petrovskii-piskunov equation, Nonlinear Anal. TMA, 71, 11, 5724-5732, (2009) · Zbl 1180.35134 [5] Kudryashov, N. A., Exact solitary waves of the Fisher equation, Phys. Lett. A, 342, 1-2, 99-106, (2005) · Zbl 1222.35054 [6] Vitanov, N. K.; Jordanov, I. P.; Dimitrova, Z. I., On nonlinear population waves, Appl. Math. Comput., 215, 8, 2950-2964, (2009) · Zbl 1181.92083 [7] Murray, J. D., Mathematical biology. I. an introduction, 556, (2001), Springer-Verlag [8] Aronson, D. G.; Weinberger, H. F., Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Partial Differ. Eq. Relat. Top., 446, 5-49, (1975) · Zbl 0325.35050 [9] Kudryashov, N. A., Exact solutions of the Burgers-Huxley equation, J. Appl. Math. Mech., 68, 3, 413-420, (2004) · Zbl 1092.35084 [10] Feng, Z. A.; Tian, J. A.; Zheng, S. B.; Lu, H. B., Travelling wave solutions of the Burgers-Huxley equation, IMA J. Appl. Math. (Institute of Mathematics and its Applications), 77, 3, 316-325, (2012) · Zbl 1250.35152 [11] Malfliet, W.; Hereman, W., The tanh method: I. exact solutions of nonlinear evolution and wave equations, Phys. Scr., 54, 563-568, (1996) · Zbl 0942.35034 [12] Parkes, E. J.; Duffy, B. R., An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations, Comput. Phys. Comm., 98, 288-300, (1996) · Zbl 0948.76595 [13] Biswas, A., Solitary wave solution for the generalized Kawahara equation, Appl. Math. Lett., 22, 208-210, (2009) · Zbl 1163.35468 [14] Kudryashov, N. A., Exact solutions of the generalized Kuramoto-Sivashinsky equation, Phys. Lett. A, 147, 287-291, (1990) [15] Kudryashov, N. A., Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos Solitons Fractals, 24, 1217-1231, (2005) · Zbl 1069.35018 [16] Vitanov, N. K., Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity, Commun. Nonlinear Sci. Numer. Simul., 15, 2050-2060, (2010) · Zbl 1222.35062 [17] Wang, M. L.; Li, X.; Zhang, J., The \(G^\prime / G\)-expansion method and evolution equation in mathematical physics, Phys. Lett. A, 372, 417-421, (2008) [18] Kudryashov, N. A., A note on the \(G^\prime / G\)-expansion method, Appl. Math. Comput., 217, 1755-1758, (2010) · Zbl 1203.35228 [19] Kudryashov, N. A., One method for finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul., 17, 2248-2253, (2012) · Zbl 1250.35055 [20] Kudryashov, N. A., Polynomials in logistic function and solitary waves of nonlinear differential equations, Appl. Math. Comput., 219, 9245-9253, (2013) · Zbl 1297.35076 [21] Polyanin, A. D.; Zaitsev, V. F., Handbook of nonlinear partial differential equations, (2011), Chapman and Hall/CRC Boca Raton · Zbl 1024.35001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.