Abstract
Our objective is to develop a calculation technique that allows performing an effective algebro-geometric (group) analysis of partial differential equations with arbitrarily many independent variables. We completely describe an important class of multidimensional evolution equations admitting Backlund correspondences of a given form. In particular, this class is found to be rather wide, although it turns out to be somewhat richer in the one-dimensional case because the requirement that mixed derivatives be equal is absent.
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