Generalization of SUSY intertwining relations: New exact solutions of Fokker-Planck equation

It is commonly known that the Fokker-Planck equation is exactly solvable only for some particular systems, usually with time-independent drift coefficients. To extend the class of solvable problems, we use the intertwining relations of SUSY Quantum Mechanics but in new -asymmetric- form. It turns out that this form is just useful for the solution of the Fokker-Planck equation. As usual, intertwining provides a partnership between two different systems both described by the Fokker-Planck equation. Due to the use of an asymmetric kind of intertwining relations with a suitable ansatz, we managed to obtain a new class of analytically solvable models. What is important, this approach allows us to deal with the drift coefficients depending on both variables, x and t. An illustrating example of the proposed construction is given explicitly.