The generalized Kupershmidt deformation for constructing new discrete integrable systems

Abstract

KdV6 equation can be described as the Kupershmidt deformation of the KdV equation (see 2008, Phys. Lett. A 372: 263). In this paper, starting from the bi-Hamiltonian structure of the discrete integrable system, we propose a generalized Kupershmidt deformation to construct new discrete integrable systems. Toda hierarchy, Kac-van Moerbeke hierarchy and Ablowitz-Ladik hierarchy are considered. The Lax representations for these new deformed systems are presented. The generalized Kupershmidt deformation for the discrete integrable systems provides a new way to construct new discrete integrable systems.

16 pages. Accepted by Theoretical and Mathematical Physics

References in corpus (6)

• KdV6: An Integrable System
• A new integrable generalization of the Korteweg - de Vries equation
• Nonholonomic deformation of KdV and mKdV equations and their symmetries, hierarchies and integrability
• The bi-Hamiltonian structure and new solutions of KdV6 equation
• The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons
• The generalized Kupershmidt deformation for constructing new integrable systems from integrable bi-Hamiltonian systems