Reduction operators of variable coefficient semilinear diffusion equations with a power source

TL;DR

This paper investigates reduction operators, also known as nonclassical symmetries, of variable coefficient semilinear reaction-diffusion equations with power nonlinearities, using a specific algorithm to classify these symmetries.

Contribution

The paper applies an existing algorithm to classify reduction operators of a class of variable coefficient reaction-diffusion equations with power nonlinearities.

Findings

Classification of reduction operators for the equations.

Identification of conditions under which nonclassical symmetries exist.

Extension of previous symmetry analysis methods.

Abstract

Reduction operators (called often nonclassical symmetries) of variable coefficient semilinear reaction-diffusion equations with power nonlinearity $f(x)u_t=(g(x)u_x)_x+h(x)u^m$ ($m\neq0,1,2$) are investigated using the algorithm suggested in [O.O. Vaneeva, R.O. Popovych and C. Sophocleous, Acta Appl. Math., 2009, V.106, 1-46; arXiv:0708.3457].