SUSY缠绕关系的推广：Fokker-Planck方程的新精确解
Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation
摘要：
众所周知，Fokker-Planck方程仅对某些特定的系统是精确可解的，通常具有与时间无关的漂移系数。为了推广这类可解问题，我们使用了超对称量子力学中的缠绕关系，但采用了新的非对称形式.结果表明，这种形式正好适用于求解福克-普朗克方程。通常，缠绕提供了两个不同系统之间的伙伴关系，这两个系统都由福克-普朗克方程描述。由于使用了一种非对称的交织关系与适当的Anterior，我们设法获得了一类新的解析可解模型。重要的是，这种方法使我们能够处理的漂移系数取决于两个变量，$x,$和$t.$一个说明性的例子，所提出的建设明确给出。
英文摘要：
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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