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

Authors：Ma, Wen-Xiu^*

Source：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149(1): 251-263.

DOI：10.1090/proc/15174

• Nonlocal reverse-spacetime integrable equation
• Riemann-Hilbert problem
• inverse scattering transform
• soliton solution
• parity-time symmetry

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.

• Institution
  浙江师范大学; 西北大学