Transmutations of supersymmetry through soliton scattering and self-consistent condensates

Abstract

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 Schrodinger operators. The ordinary N=2 supersymmetry for such Schrodinger 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 non-standard 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 Bogoliubov-de Gennes and Gross-Neveu models, and indicate the exotic N=4 nonlinear supersymmetry of the paired reflectionless Dirac systems.