Similarity solution of the evolution equation describing the combined effects of diffusion and recombination in plasmas

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Abstract
The evolution equation accounting for effects of diffusion and recombination is transformed into a similarity equation in one, two, and three dimensions. This equation does not fulfil the Painlevé criterion and thus cannot be directly classified, or its properties analyzed, in general terms of its singularities. A particular similarity solution can, however, be constructed. It allows for a description of the evolution of plasma configurations of physical significance.