Resumen de Bäcklund transformations for Darboux integrable differential systems

Michael T. Anderson, M.E. Fels

• The purpose of this paper is to present a novel group-theoretic method for constructing Bäcklund transformations between systems of differential equations. Our approach is based upon the definition of Bäcklund transformations as integrable extensions of exterior differential systems. The construction of these transformations is obtained using the general theory of symmetry reduction of differential systems. Our method is then applied to differential systems which are integrable by the method of Darboux, and a detailed understanding of the Bäcklund transformations for these systems is obtained.