Inverse scattering transforms and soliton solutions of nonlocal reverse-space nonlinear Schrodinger hierarchies

作者：Ma, Wen-Xiu^*; Huang, Yehui; Wang, Fudong

来源：Studies in Applied Mathematics, 2020, 145(3): 563-585.

DOI：10.1111/sapm.12329

• integrable hierarchy
• inverse scattering
• matrix eigenvalue problem
• nonlocal reduction
• Riemann-Hilbert problem
• soliton solution

The aim of the paper is to construct nonlocal reverse-space nonlinear Schrodinger (NLS) hierarchies through nonlocal group reductions of eigenvalue problems and generate their inverse scattering transforms and soliton solutions. The inverse scattering problems are formulated by Riemann-Hilbert problems which determine generalized matrix Jost eigenfunctions. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A solution formulation to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless transforms, is presented and applied toN-soliton solutions of the nonlocal NLS hierarchies.

• 单位
  浙江师范大学; 西北大学