Eur. Phys. J. B 79, 79-84 (2011)
https://doi.org/10.1140/epjb/e2010-90983-8

Exact analytical solutions for nonlinear waves in the inhomogeneous Fisher-Kolmogorov equation

¹ Department of Physics and Astronomy, University of New Mexico, 800 Yale Blvd, Albuquerque, NM, 87131, USA
² Physics Faculty, Moscow State University, Vorob'evy Gory, 119992 Moscow, Russia

Corresponding author: ^a zemskov@brandeis.edu

Received: 18 December 2009
Revised: 31 October 2010
Published online: 10 December 2010

Abstract

Exact analytical solutions of the reaction-diffusion equations with spatial inhomogeneous reaction and diffusion coefficients are found. It is shown that the space-oscillating approximate solution of a traveling wave type [P.K. Brazhnik, J.J. Tyson, SIAM J. Appl. Math. 60, 371 (1999)] is the exact one for the inhomogeneous Fisher-Kolmogorov equation in two dimensions.