Painlevé analysis and special solutions of two families of reaction—diffusion equations

Abstract A Painleve analysis is performed for two families of reaction—diffusion equations. Truncated expansions, relevant to equations having movable branch points at leading order, are used to construct special solutions for the two classes of reaction—diffusion equations. An auto-Backlund transformation between two solutions is constructed for an equation having a pole at leading order, leading to additional analytic solutions.

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