Darboux Transformation for Dirac Equations with (1+1) potentials
A.V. Yurov
TL;DR
This paper explores the Darboux transformation for (1+1)-dimensional Dirac equations, constructing exact solutions and linking them to soliton solutions of the Davey--Stewartson equations, advancing methods for solving such quantum systems.
Contribution
It introduces a Darboux transformation approach for Dirac equations with (1+1) potentials and connects these solutions to soliton solutions of integrable equations.
Findings
Exact solutions for Dirac equations with external fields are constructed.
A connection between Dirac potentials and Davey--Stewartson solitons is established.
The method enhances solvability of Dirac equations with specific potentials.
Abstract
We study the Darboux transformation (DT) for Dirac equations with (1+1) potentials. Exact solutions for the adiabatic external field are constructed. The connection between the exactly soluble Dirac (1+1) potentials and the soliton solutions of the Davey--Stewartson equations is discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.