Non-Hermitian matrix Schr dinger equation: B cklund–Darboux transformation, Weyl functions and symmetry

Abstract

The non-Hermitian matrix Schrodinger equation obtained by the Backlund–Darboux transformation (BDT) is treated. The potentials, fundamental solutions and Weyl functions are constructed explicitly. A symmetric reduction of the BDT is introduced and this case is studied in greater detail, including potentials, fundamental solutions, bound states, the reality of the discrete spectrum and spontaneous break of the symmetry, the sign-indefinite scalar product, and examples.