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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations
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by Wen-Xiu Ma PDF
Proc. Amer. Math. Soc. 149 (2021), 251-263 Request permission


The paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrödinger (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.
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Additional Information
  • Wen-Xiu Ma
  • Affiliation: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China; Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Mathematics and Statistics, University of South Florida, Tampa, Florida 33620; School of Mathematics, South China University of Technology, Guangzhou 510640, China; and Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa
  • MR Author ID: 247034
  • ORCID: 0000-0001-5309-1493
  • Email:
  • Received by editor(s): November 11, 2019
  • Received by editor(s) in revised form: April 8, 2020, and May 7, 2020
  • Published electronically: October 16, 2020
  • Additional Notes: This work was supported in part by NSFC under the grants 11975145 and 11972291, NSF under the grant DMS-1664561, and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB 110020).
  • Communicated by: Mourad E. H. Ismail
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 251-263
  • MSC (2010): Primary 37K15, 35Q55, 37K40
  • DOI:
  • MathSciNet review: 4172602