The generalized Kupershmidt deformation for constructing new discrete integrable systems

It is known that the KdV6 equation can be represented as the Kupershmidt deformation of the KdV equation. We propose a generalized Kupershmidt deformation for constructing new discrete integrable systems starting from the bi-Hamiltonian structure of a discrete integrable system. We consider the Toda, Kac–van Moerbeke, and Ablowitz–Ladik hierarchies and obtain Lax representations for these new deformed systems. The generalized Kupershmidt deformation provides a new way to construct discrete integrable systems.