Bäcklund Transformations and Recursion Operators via Symmetry

Abstract

In this paper we study interrelations between the Lax-formulation, Bäcklund transformations and recursion operators. It is shown that different integrability conditions can be connected via Lie-Bäcklund symmetries of the Lax-formulation. This is then used to derive Bäcklund transformations and recursion operators for various equations.