Lie-algebraic approach for the Fokker–Planck equation with a nonlinear drift force

In this paper we have investigated the algebraic structure of the Fokker–Planck equation with a nonlinear drift force. Using the Lie-algebraic approach we have obtained an exact form of the time evolution operator which, in turn, enables us to derive the propagator readily. Since the propagator is for a very general Fokker–Planck equation with a nonlinear drift force, results for any special case can be easily deduced from it.