On the quantum inverse problem for a new type of nonlinear Schroedinger equation for Alfven waves in plasma

The nonlinear Alfven waves are governed by the Vector Derivative Nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the quantum inverse problem for a new type of nonlinear Schroedinger equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states.