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Solutions and Conditional Lie–Bäcklund Symmetries of Quasi-linear Diffusion-Reaction Equations

New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Bäcklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.