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


Author: Wen-Xiu Ma
Journal: Proc. Amer. Math. Soc. 149 (2021), 251-263
MSC (2010): Primary 37K15, 35Q55, 37K40
DOI: https://doi.org/10.1090/proc/15174
Published electronically: October 16, 2020
MathSciNet review: 4172602
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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.


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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: mawx@cas.usf.edu

Keywords: Nonlocal reverse-spacetime integrable equation, Riemann-Hilbert problem, inverse scattering transform, soliton solution, parity-time symmetry
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
Article copyright: © Copyright 2020 American Mathematical Society