Reduction operators of variable coefficient semilinear diffusion equations with an exponential source

Abstract

Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ are investigated using the algorithm involving a mapping between classes of differential equations, which is generated by a family of point transformations. A special attention is paid for checking whether reduction operators are inequivalent to Lie symmetry operators. The derived reduction operators are applied to construction of exact solutions.