On the Geometry of Bäcklund Transformations

Abstract

The geometry of an admissible Bäcklund transformation for an exterior differential system is described by an admissible Cartan connection for a geometric structure on a tower with infinite--dimensional skeleton which is the universal prolongation of a $|1|$--graded semi-simple Lie algebra.

4 pages, Proc. Int. Workshop on Nonlinear Physics (Gallipoli, 2002), v2:comment field changed

Cited by in corpus (2)

• Bäcklund loop algebras for compact and non-compact nonlinear spin models in $(2+1)$ dimensions
• Constructing towers with skeletons from open Lie algebras and integrability