Abstract
New classes of the exact solutions of nonlinear diffusion equations are constructed.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
REFERENCES
R. A. Fisher, “The wave of advance of advantageous genes,” Ann. Eugenics, 7, 353–369 (1937).
J. D. Marrey, Mathematical Biology, Springer, Berlin (1989).
M. I. Serov and R. M. Cherniha, “Lie symmetries and exact solutions of nonlinear heat equations with convection term,” Ukr. Mat. Zh., 49, No.9, 1262–1270 (1997).
R. Cherniha and M. Serov, “Lie and non-Lie symmetries of nonlinear diffusion equations with convection term,” i n: Proceedings of the Second International Conference “Symmetry in Nonlinear Mathematical Physics,” Vol. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (1997), pp. 444–449.
A. G. Nikitin and T. A. Barannyk, “Solitary wave and other solutions for nonlinear heat equations,” math-ph/0304004.
V. I. Fushchich, V. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).
L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).
D. Levi and P. Winternitz, “Nonclassical symmetry reduction: example of the Boussinesq equation,” J. Phys. A: Math. Gen., 22, 2915–2924 (1989).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1011 – 1019, August, 2005.
Rights and permissions
About this article
Cite this article
Barannyk, A.F., Yuryk, I.I. On Exact Solutions of Nonlinear Diffusion Equations. Ukr Math J 57, 1189–1200 (2005). https://doi.org/10.1007/s11253-005-0256-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-005-0256-x