Multi-parameter isospectral Fokker-Planck equations

TL;DR

This paper introduces a method to generate multi-parameter deformations of Fokker-Planck equations using Darboux-Crum transformations, extending to fractional cases and discussing applications in black hole physics.

Contribution

It presents a novel approach to construct multi-parameter isospectral Fokker-Planck equations via Darboux-Crum transformations, including fractional extensions.

Findings

Constructed multi-parameter deformed Fokker-Planck equations.

Extended the method to fractional Fokker-Planck equations.

Commented on applications to black hole models.

Abstract

From a given Fokker-Planck equation, a multi-parameter deformed partner Fokker-Planck equation is constructed. This is done by first deleting a set of eigenstates of the original FPE by the multi-step Darboux-Crum transformation, and then reinstating the eigen-energy levels by the reverse Darboux-Crum transformation. Extension to fractional Fokker-Planck equation is briefly discussed. A recent study of the one-parameter isospectral FPE applied to black hole in the thermal potential approach is commented.