Mathematical Physics
[Submitted on 8 Sep 2021
(v1)
, last revised 13 Mar 2024 (this version, v2)]
Title: Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations
Title: 时变Darboux变换与Fokker-Planck方程的超对称层次结构
Abstract: A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schr\"odinger equation. The formalism of supersymmetric quantum mechanics is extended by applying the Darboux transformation directly to the non-stationary Schr\"odinger equation. From a solution of a Fokker-Planck equation a solution of the Darboux partner is obtained. For drift coefficients satisfying the condition of shape invariance, a supersymmetric hierarchy of Fokker-Planck equations with solutions related by the Darboux transformation is obtained.
Submission history
From: Choon-Lin Ho [view email][v1] Wed, 8 Sep 2021 18:09:03 UTC (12 KB)
[v2] Wed, 13 Mar 2024 19:03:43 UTC (12 KB)
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