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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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
