NONPERTURBATIVE STUDIES OF A QUANTUM HIGHER-ORDER NONLINEAR SCHRODINGER MODEL USING THE BETHE-ANSATZ

We consider the integrability problem for a quantum version of the per turbed nonlinear Schrodinger (NS) equation, including a higher spatial dispersion and nonlinear dispersion of the group velocity (the corres ponding classical equations are well known in the nonlinear fiber opti cs and in other applications). Employing the Bethe ansatz (BA) techniq ue, which is known to yield a complete spectrum including the so-calle d quantum solitons (multiparticle bound states) of the unperturbed NS system, we find that the particular cases of the model which correspon d to integrable classical equations, viz., the derivative NS and Hirot a equations, are also fully integrable at the quantum level. In the ge neric (nonintegrable) case, the model remains integrable in the two-pa rticle sector. In the three-particle sector, the BA produces unphysica l states with complex energy. It turns out that the Hamiltonian in thi s case becomes non-Hermitian. We propose a procedure for finding the p hysical eigenstates of the system. We build an example of such a state and we show that it describes inelastic scattering.