Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation

• URL: http://arxiv.org/abs/2004.03980v1
• Date: Wed, 8 Apr 2020 12:56:36 GMT
• Title: Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation
• Authors: M. V. Ioffe, D. N. Nishnianidze
• Abstract summary: A new class of analytically solvable models is presented for Fokker-Planck equation. What is important, this approach allows us to deal with the drift coefficients depending on both variables.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 solution of Fokker-Planck equation. As usual, intertwining provides a partnership between two different systems both described by 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.

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