ON ONE-PARAMETRIC FAMILIES OF B\"{A}CKLUND TRANSFORMATIONS

Author: Joseph KRASIL'SHCHIK

In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of B{\"a}cklund transformations is given. It is shown that any family of such a kind evolves in the direction of a nonlocal symmetry shadow in the sense of Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and B\"{a}cklund transformations by I.S. Krasil'shchik and A.M. Vinogradov (Acta Appl. Math., 15 (1989) no.1-2, 161-209). In addition, a formal family naturally corresponding to a shadow is described.

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