Steady State Solutions of the Fokker-Planck Equations

A new way of constructing the steady state solutions of the Fokker-Planck Equations(FPE's) is described in which the concept of a vortex field plays an important role. The steady state solutions can be classified according to the type of . In particular, one easily obtains almost all the exact global solutions known so far for the stationary FPE's, as well as the exact local solutions near the fixed points of the corresponding deterministic equations. In this way some new properties of FPE are explored.