数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 127-140.doi: 10.1007/s10473-022-0106-z

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RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

马文秀1,2,3,4   

  1. 1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China;
    2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia;
    3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA;
    4. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa
  • 收稿日期:2020-08-20 出版日期:2022-02-25 发布日期:2022-02-24
  • 作者简介:Wenxiu MA,E-mail:mawx@cas.usf.edu
  • 基金资助:
    The work was supported in part by NSFC (11975145 and 11972291), and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB 110020).

RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

Wenxiu MA1,2,3,4   

  1. 1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China;
    2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia;
    3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA;
    4. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa
  • Received:2020-08-20 Online:2022-02-25 Published:2022-02-24
  • Supported by:
    The work was supported in part by NSFC (11975145 and 11972291), and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB 110020).

摘要: The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrödinger (NLS) hierarchies associated with higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless inverse scattering transforms, is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.

关键词: matrix spectral problem, nonlocal reverse-time integrable equation, integrable hierarchy, Riemann-Hilbert problem, inverse scattering transform, soliton solution

Abstract: The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrödinger (NLS) hierarchies associated with higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless inverse scattering transforms, is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.

Key words: matrix spectral problem, nonlocal reverse-time integrable equation, integrable hierarchy, Riemann-Hilbert problem, inverse scattering transform, soliton solution

中图分类号: 

  • 37K15