INVERSE SCATTERING AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-SPACETIME NONLINEAR SCHRODINGER EQUATIONS

The paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrodinger (NLS) equations under a specific nonlocal group reduction, and generates their inverse scattering transforms and soliton solutions by the Riemann-Hilbert technique. The Sokhotski-Plemelj formula is used to determine solutions to a class of associated Riemann-Hilbert problems and transform the systems that generalized Jost solutions need to satisfy. A formulation of solutions is developed for the Riemann-Hilbert problems associated with the reflectionless transforms, and the corresponding soliton solutions are constructed for the presented nonlocal reverse-spacetime PT-symmetric NLS equations.

Automated summary

This paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrodinger equations and their inverse scattering transforms and soliton solutions using the Riemann-Hilbert technique under a specific nonlocal group reduction. The Sokhotski-Plemelj formula is used to determine solutions to a class of associated Riemann-Hilbert problems and transform the systems that generalized Jost solutions need to satisfy. A formulation of solutions is developed for the Riemann-Hilbert problems associated with the reflectionless transforms, and soliton solutions are constructed for the presented nonlocal reverse-spacetime PT-symmetric NLS equations.