A Novel Hierarchy of Integrable Lattices

Abstract

In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector generalisation. We also solve the associated spectral problem and explicity contruct action-angle variables through the r-matrix approach.