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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