On nonclassical symmetries of generalized Huxley equations

Abstract

Nonclassical symmetries of a class of generalized Huxley equations of form $u_t=u_{xx}+k(x)u^2(1-u)$ are found. More precisely, for the class under consideration we completely classify reduction operators with $\tau =1$ and give a wide number of examples of equations admitting reduction operators with $\tau =0$.

contribution to the Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (4 - 10 June 2010, Protaras, Cyprus)