Liouville Correspondences between Integrable Hierarchies

Abstract

In this paper, we study explicit correspondences between the integrable Novikov and Sawada-Kotera hierarchies, and between the Degasperis-Procesi and Kaup-Kupershmidt hierarchies. We show how a pair of Liouville transformations between the isospectral problems of the Novikov and Sawada-Kotera equations, and the isospectral problems of the Degasperis-Procesi and Kaup-Kupershmidt equations relate the corresponding hierarchies, in both positive and negative directions, as well as their associated conservation laws. Combining these results with the Miura transformation relating the Sawada-Kotera and Kaup-Kupershmidt equations, we further construct an implicit relationship which associates the Novikov and Degasperis-Procesi equations.

References in corpus (6)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Inverse Scattering Transform for the Camassa-Holm equation
• Inverse Scattering Transform for the Degasperis-Procesi Equation
• Dressing Method for the Degasperis-Procesi Equation
• Generalisations of the Camassa-Holm equation
• Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy

Cited by in corpus (1)

• Unfamiliar Aspects of Bäcklund Transformations and an Associated Degasperis-Procesi Equation