Darboux transformation for a general Dirac equation in two dimensions
Ekaterina Pozdeeva, Axel Schulze-Halberg
TL;DR
This paper develops explicit Darboux transformations for a general two-dimensional Dirac equation, extending previous one-dimensional results and applicable in cylindrical coordinates with practical examples.
Contribution
It introduces a generalized Darboux transformation framework for 2D Dirac equations, unifying and extending earlier 1D and (1+1)D cases.
Findings
Transformations applicable in cylindrical coordinates
Extension of 1D and (1+1)D results
Multiple explicit examples provided
Abstract
We construct explicit Darboux transformations for a generalized, two-dimensional Dirac equation. Our results contain former findings for the one-dimensional, stationary Dirac equation, as well as for the fully time-dependent case in (1+1) dimensions. We show that our Darboux transformations are applicable to the two-dimensional Dirac equation in cylindrical coordinates and give several examples.
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