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

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.

💡 Research Summary

The paper investigates nonclassical (also called Q‑conditional or reduction) symmetries of a broad class of variable‑coefficient semilinear reaction‑diffusion equations of the form
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