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

Abstract

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.