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

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].

💡 Research Summary

The paper addresses the problem of finding nonclassical symmetries (also called reduction operators) for a broad class of one‑dimensional reaction‑diffusion equations with variable coefficients and a power‑type source term:

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