2014/01/31 by Adrian Arancibia, Adrián Arancibia, Mikhail S. Plyushchay · 1 citation
Mathematics · Physics and Astronomy · #Dirac (video compression format) #Dirac operator #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Scalar (mathematics) #Soliton #Superspace #Supersymmetry #Theoretical physics #hep-th #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1103/physrevd.90.025008
published as Phys. Rev. D 90, 025008 (2014) · 26 pages, 4 figures; refs and comments added
openalex publication_date 2014/07/07 · arxiv created 2014/07/08 · arxiv updated 2014/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the two most general families of the (1+1)D Dirac systems with transparent scalar potentials and two related families of the paired reflectionless Schr"odinger operators. The ordinary N=2 supersymmetry for such Schr"odinger pairs is enlarged up to an exotic N=4 nonlinear centrally extended supersymmetric structure, which involves two bosonic integrals composed from the Lax-Novikov operators for the stationary Korteweg--de Vries hierarchy. Each associated single Dirac system displays a proper N=2 nonlinear supersymmetry with a nonstandard grading operator. One of the two families of the first- and second-order systems exhibits the unbroken supersymmetry, while another is described by the broken exotic supersymmetry. The two families are shown to be mutually transmuted by applying a certain limit procedure to the soliton scattering data. We relate the topologically trivial and nontrivial transparent potentials with self-consistent inhomogeneous condensates in the Bogoliubov--de Gennes and Gross-Neveu models and indicate the exotic N=4 nonlinear supersymmetry of the paired reflectionless Dirac systems.