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A symmetry group classification for fourth-order reaction-diffusionequations, allowing for both second-order and fourth-order diffusion terms, iscarried out. The fourth order equations are treated, firstly, as systems ofsecond-order equations that bear some resemblance to systems of coupledreaction-diffusion equations with cross diffusion, secondly, as systems of asecond-order equation and two first-order equations. The paper generalizes theresults of Lie symmetry analysis derived earlier for particular cases of theseequations. Various exact solutions are constructed using Lie symmetryreductions of the reaction-diffusion systems to ordinary differentialequations. The solutions include some unusual structures as well as thefamiliar types that regularly occur in symmetry reductions, namely self-similarsolutions, decelerating and decaying traveling waves, and steady states.

Lie Symmetries and Exact Solutions of the Generalized Thin Film Equation