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 $\tau=0$.