Exact solutions of nonlinear Fokker-Planck equations of the Desai-Zwanzig type

By means of time-dependent similarity transformations, we derive exact solutions of the Fokker-Planck equations with time-dependent drifts depending on process mean values. The method of similarity transformation is simple and can be easily applied to more general Fokker-Planck equations. Furthermore, the knowledge of the exact solutions in closed form can be useful as a benchmark to test approximate numerical or analytical procedures.