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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 210, Number 3, Pages 387–404
DOI: https://doi.org/10.4213/tmf10194 (Mi tmf10194) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On the Riemann–Hilbert problem of the matrix Lakshmanan–Porsezian–Daniel system with a $4\times4$ AKNS-type matrix Lax pair

Beibei Huab, Xiaomei Yua, Ling Zhanga

a School of Mathematics and Finance, Chuzhou University, Chuzhou, Anhui, China
b Department of Physics, Zhejiang Normal University, Jinhua, Zhejiang, China
Full-text PDF (523 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf10194
Abstract: The initial-boundary value problems for the matrix Lakshmanan–Porsezian–Daniel system are studied by utilizing the Fokas unified transform approach. First, the spectral analysis of the $4\times4$ Ablowitz–Kaup–Newell–Segur-type matrix Lax pair is performed. Second, solutions of the matrix Lakshmanan–Porsezian–Daniel system are reconstructed from a $4\times4$ matrix Riemann–Hilbert problem. It is proved in addition that the spectral functions are not independent but are related by the so-called global relation.
Keywords: Volterra integral equations, Riemann–Hilbert problem, matrix Lakshmanan–Porsezian–Daniel system, initial-boundary value problem, Fokas unified transform approach.
Funding agency Grant number
National Natural Science Foundation of China 12147115
11975145
Natural Science Foundation of Anhui Province 2108085QA09
Natural Science Research Project of Colleges and Universities in Anhui Province KJ2021A1094
KJ2021B03
This work was supported by the National Natural Science Foundation of China under the grants 12147115 and 11975145, the Natural Science Foundation of Anhui Province under the grant 2108085QA09, and the Natural Science Research Project of Colleges and Universities in Anhui Province under the grant KJ2021A1094 and KJ2021B03.
Received: 08.11.2021
Revised: 30.12.2021
Published: 27.02.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 210, Issue 3, Pages 337–352
DOI: https://doi.org/10.1134/S0040577922030047
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik, 02.20.Sv
MSC: 35G31, 35Q15, 37K10, 45D05.
Language: Russian
Citation: Beibei Hu, Xiaomei Yu, Ling Zhang, “On the Riemann–Hilbert problem of the matrix Lakshmanan–Porsezian–Daniel system with a $4\times4$ AKNS-type matrix Lax pair”, TMF, 210:3 (2022), 387–404; Theoret. and Math. Phys., 210:3 (2022), 337–352
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
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