A SIMPLE LATTICE VERSION OF THE NONLINEAR SCHRODINGER-EQUATION AND ITS DEFORMATION WITH AN EXACT QUANTUM SOLUTION

A lattice version of the quantum nonlinear Schrodinger (NLS) equation is considered, which has a significant simple form and fulfils most of the criteria desirable for such lattice variants of field models. Unl ike most of the known lattice NLs equations, the present model belongs to a class which does not exhibit the usual symmetry properties. Howe ver, this lack of symmetry itself seems to be responsible for the rema rkable simplification of the relevant objects in the theory, such as t he Lax operator, the Hamiltonian and other commuting conserved quantit ies as well as their spectra. The model allows exact quantum solution through the algebraic Bethe ansatz and also a straightforward and natu ral generalization to the vector case, thus giving a new exact lattice version of the vector NLS model. A deformation representing a new qua ntum integrable system involving Tamm-Dancoff-like q-boson operators i s constructed.