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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 219, Number 3, Pages 462–473
DOI: https://doi.org/10.4213/tmf10682 (Mi tmf10682) 		 
A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources and dynamics

Qi Lia, Qiu-yuan Duanb

a Department of Mathematics, East China University of Technology, Nanchang, China
b Department of Mathematics, Fuzhou Vocational College of Technology, Fuzhou, China
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DOI: https://doi.org/10.4213/tmf10682
Abstract: A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources is introduced. The physically significant nonlinear equation is associated with the AKNS spectral problem. In the nonlocal case, the squared eigenfunction of the $L$ operator leads to some changes in the term of the source that affect the motion of solitons. The soliton solutions of the nonlocal nonlinear Schrödinger equation with self-consistent sources are presented using the inverse scattering transform. The dynamics of the solitons are illustrated, which differ from those of the nonlocal equation without a source.
Keywords: self-consistent source, inverse scattering transform, nonlocal nonlinear Schrödinger equation, dynamics.
Funding agency Grant number
National Natural Science Foundation of China 11561002
11861006
This project is supported by the National Natural Science Foundation of China (grant Nos. 11561002 and 11861006).
Received: 28.01.2024
Revised: 28.01.2024
English version:
Theoretical and Mathematical Physics, 2024, Volume 219, Issue 3, Pages 933–943
DOI: https://doi.org/10.1134/S0040577924060047
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik, 05.45.Yv
Language: Russian
Citation: Qi Li, Qiu-yuan Duan, “A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources and dynamics”, TMF, 219:3 (2024), 462–473; Theoret. and Math. Phys., 219:3 (2024), 933–943
Citation in format AMSBIB
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\crossref{https://doi.org/10.1134/S0040577924060047}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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