On reciprocal properties of the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt hierarchies

Abstract

New hierarchies of nonlinear evolution equations are introduced which are linked by reciprocal transformations to the Caudrev-Dodd-Gibbon and Kaup-Kupershmidt sequences. Invariance under a Möbius transformation of the singularity manifold equations for these sequences leads to a novel generic invariance properly of the new systems. The latter have as base members Kawamoto-type equations. Explicit auto-Bäcklund transformations for the Caudry-Dodd-Gibbon and Kaup-Kuperschmidt hierarchies are generated via a reciprocal property.