Multi-band structure of the quantum bound states for a generalized nonlinear Schrodinger model

By using the method of coordinate Bethe ansatz, we study N-body bound states of a generalized nonlinear Schrodinger model having two real coupling constants c and \eta. It is found that such bound states exist for all possible values of c and within several nonoverlapping ranges (called bands) of \eta. The ranges of \eta within each band can be determined completely using Farey sequences in number theory. We observe that N-body bound states appearing within each band can have both positive and negative values of the momentum and binding energy.