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Riemann-Hilbert problems and soliton solutions of nonlocal reverse-time NLS hierarchies

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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.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Wenxiu Ma

  2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Wenxiu Ma

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wenxiu Ma

  4. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wenxiu Ma

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  1. Wenxiu Ma
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Correspondence to Wenxiu Ma.

Additional information

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).

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Ma, W. Riemann-Hilbert problems and soliton solutions of nonlocal reverse-time NLS hierarchies. Acta Math Sci 42, 127–140 (2022). https://doi.org/10.1007/s10473-022-0106-z

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  • DOI: https://doi.org/10.1007/s10473-022-0106-z

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