The Kerr medium as an SU(2) system: exact solution for spin damping

The non-linear Kerr medium in the presence of damping and earlier associated with an SU(1,1) symmetry, is exactly solved as a spin damped system, associated with an SU(2) symmetry. The association with SU(2) is exploited to express the dynamics of the system as a Schrödinger-like equation, whose solution is obtained using the appropriate disentanglement theorem. This method is then extended to multi-mode coupled nonlinear oscillators for obtaining exact solutions.