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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 210, Number 1, Pages 38–53
DOI: https://doi.org/10.4213/tmf10150 (Mi tmf10150) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Inverse scattering transform for a nonlocal derivative nonlinear Schrödinger equation

Xinxin Maa, Yonghui Kuangb

a Department of Mathematics, School of Science, China University of Mining and Technology, Beijing, China
b College of Science, Zhongyuan University of Technology, Zhengzhou, China
Full-text PDF (536 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf10150
Abstract: We give a detailed discussion of a nonlocal derivative nonlinear Schrödinger (NL-DNLS) equation with zero boundary conditions at infinity in terms of the inverse scattering transform. The direct scattering problem involves discussions of the analyticity, symmetries, and asymptotic behavior of the Jost solutions and scattering coefficients, and the distribution of the discrete spectrum points. Because of the symmetries of the NL-DNLS equation, the discrete spectrum is different from those for DNLS-type equations. The inverse scattering problem is solved by the method of a matrix Riemann–Hilbert problem. The reconstruction formula, the trace formula, and explicit solutions are presented. The soliton solutions with special parameters for the NL-DNLS equation with a reflectionless potential are obtained, which may have singularities.
Keywords: nonlocal derivative nonlinear Schrödinger equation, zero boundary conditions, symmetry properties, matrix Riemann–Hilbert problem, singularity.
Funding agency Grant number
National Natural Science Foundation of China 11931017
12001560
Yue Qi Young Scholar Project, China University of Mining and Technology 00-800015Z1201
Fundamental Research Funds for the Central Universities of China 00-800015A566
This work was supported by the National Natural Science Foundation of China (NNSFC) (Grant Nos. 11931017 and 12001560), the Yue Qi Young Scholar Project, China University of Mining and Technology, Beijing (Grant No. 00-800015Z1201), and the Fundamental Research Funds for Central Universities (Grant No. 00-800015A566).
Received: 15.07.2021
Revised: 22.08.2021
English version:
Theoretical and Mathematical Physics, 2022, Volume 210, Issue 1, Pages 31–45
DOI: https://doi.org/10.1134/S0040577922010032
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Xinxin Ma, Yonghui Kuang, “Inverse scattering transform for a nonlocal derivative nonlinear Schrödinger equation”, TMF, 210:1 (2022), 38–53; Theoret. and Math. Phys., 210:1 (2022), 31–45
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    1. Xin-Yu Liu, Rui Guo, “The Riemann–Hilbert approach for the nonlocal derivative nonlinear Schrödinger equation with nonzero boundary conditions”, Z. Angew. Math. Phys., 76:1 (2025)  crossref
    2. Beibei Hu, Zuyi Shen, Ling Zhang, Fang Fang, “Riemann–Hilbert approach to the focusing and defocusing nonlocal derivative nonlinear Schrödinger equation with step-like initial data”, Applied Mathematics Letters, 148 (2024), 108885  crossref  mathscinet
    3. Shikun Cui, Zhen Wang, “Numerical inverse scattering transform for the derivative nonlinear Schrödinger equation”, Nonlinearity, 37:10 (2024), 105015  crossref
    4. Yongshuai Zhang, Deqin Qiu, Shoufeng Shen, Jingsong He, “The revised Riemann–Hilbert approach to the Kaup–Newell equation with a non-vanishing boundary condition: Simple poles and higher-order poles”, Journal of Mathematical Physics, 65:8 (2024)  crossref
    5. Xin-Yu Liu, Rui Guo, “Mixed single, double, and triple poles solutions for the space-time shifted nonlocal DNLS equation with nonzero boundary conditions via Riemann–Hilbert approach”, Nuclear Physics B, 1009 (2024), 116742  crossref
    6. Yongshuai Zhang, Haibing Wu, Deqin Qiu, “Revised Riemann–Hilbert problem for the derivative nonlinear Schrödinger equation: Vanishing boundary condition”, Theoret. and Math. Phys., 217:1 (2023), 1595–1608  mathnet  crossref  crossref  mathscinet  adsnasa
    7. Halis Yilmaz, “Binary Darboux transformation for the Gerdjikov–Ivanov equation”, Wave Motion, 113 (2022), 102991  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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