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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 1, Pages 23–43
DOI: https://doi.org/10.4213/tmf10015 (Mi tmf10015) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Riemann–Hilbert problem for the Kundu-type nonlinear Schrödinger equation with $N$ distinct arbitrary-order poles

Zi-Yi Wang, Shou-Fu Tian, Xiao-Fan Zhang

School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou, China
Full-text PDF (1018 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf10015
Abstract: We use the Riemann–Hilbert (RH) method to study the Kundu-type nonlinear Schrödinger (Kundu–NLS) equation with a zero boundary condition in the case where the scattering coefficient has $N$ distinct arbitrary-order poles. We perform a spectral analysis of the Lax pair and consider the asymptotic property, symmetry, and analyticity of the Jost solution. Based on these results, we formulate the RH problem whose solution allows solving the considered Kundu–NLS equation. In addition, using graphic analysis, we study the characteristics of soliton solutions of some particular cases of the problem with $N$ distinct arbitrary-order poles.
Keywords: Kundu–nonlinear Schrödinger equation, zero boundary condition, Riemann–Hilbert problem, arbitrary-order pole, scattering coefficient, soliton solution.
Funding agency Grant number
National Natural Science Foundation of China 11975306
Natural Science Foundation of Jiangsu Province BK20181351
Jiangsu Province JY-059
Fundamental Research Funds for the Central Universities of China 2019ZDPY07
2019QNA35
This research was supported by the National Natural Science Foundation of China (Grant No. 11975306), the Natural Science Foundation of Jiangsu Province (Grant No. BK20181351), the Six Talent Peaks Project in Jiangsu Province (Grant No. JY-059), and the Fundamental Research Fund for the Central Universities (Grant Nos. 2019ZDPY07 and 2019QNA35).
Received: 26.11.2020
Revised: 25.12.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 1, Pages 415–433
DOI: https://doi.org/10.1134/S0040577921040024
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Zi-Yi Wang, Shou-Fu Tian, Xiao-Fan Zhang, “Riemann–Hilbert problem for the Kundu-type nonlinear Schrödinger equation with $N$ distinct arbitrary-order poles”, TMF, 207:1 (2021), 23–43; Theoret. and Math. Phys., 207:1 (2021), 415–433
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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