## Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations

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- by Wen-Xiu Ma
- Proc. Amer. Math. Soc.
**149**(2021), 251-263 - DOI: https://doi.org/10.1090/proc/15174
- Published electronically: October 16, 2020
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## Abstract:

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.## References

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## Bibliographic 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: mawx@cas.usf.edu
- 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: https://doi.org/10.1090/proc/15174
- MathSciNet review: 4172602