The exact eigenstates of the Hamiltonian for a quantum three-wave interaction system with boson-fermion operators are constructed by the quantum inverse scattering method. The Bethe-ansatz equations are obtained from the periodic boundary conditions.
The generalisation of the quantum inverse scattering method is used to derive the Bethe ansatz equation of a system for a multicomponent nonlinear Schrodinger models with n species (or colours) of bosons or fermions. The matrix periodic boundary conditions for bosons and fermions are obtained and the relationship between them discussed. The eigenstates for the infinite conserved quantities of the system are constructed. Lastly, the author generalises these results to the non-linear Schrodinger model with the mirror-image delta potentials proposed by Schulz (1987).
Quantum integrability is established for the one-dimensional supersymmetric U model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric U chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system.