Borland (1998) explores the behaviour of a non-linear Fokker-Planck equation:
K = drift coefficient, Q is the diffusion constant, ν is a real number that introduces the nonlinearity, f is a probability distribution.
An equation is then derived (Langevin equation) for the actual trajectories of the system, which are a function of f.
 
Borland L. 1998. Microscopic dynamics of the nonlinear Fokker-Planck equation: A phenomenological model. Phys. Rev. E 57, 6634-442