On one-parametric families of Backlund transformations

TL;DR

This paper explores one-parametric families of Backlund transformations using cohomological deformation theory, revealing their evolution along nonlocal symmetry shadows and including classical examples.

Contribution

It provides an infinitesimal description of these families within a cohomological framework, highlighting their connection to nonlocal symmetries.

Findings

Families evolve along nonlocal symmetry shadows

Includes classical examples of Backlund transformations

Uses cohomological deformation theory for analysis

Abstract

In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of Backlund transformations of special type including classical examples is given. It is shown that any family of such a kind evolves in the direction of a nonlocal symmetry shadow.