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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 213, Number 3, Pages 437–449
DOI: https://doi.org/10.4213/tmf10290 (Mi tmf10290) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Cauchy matrix approach to the noncommutative Kadomtsev–Petviashvili equation with self-consistent sources

Zhihao Shi, Shangshuai Li, Da-jun Zhang

Shanghai University, Shanghai, China
Full-text PDF (440 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf10290
Abstract: We develop a direct method, the Cauchy matrix approach, to construct matrix solutions of noncommutative soliton equations. This approach is based on the Sylvester equation, and solutions can be presented without using quasideterminants. The matrix Kadomtsev–Petviashvili equation with self-consistent sources is employed as an example to demonstrate the approach. As a reduction, explicit solutions of the matrix Mel'nikov model for long–short wave interaction are obtained.
Keywords: self-consistent source, noncommutativity, Mel'nikov model, Cauchy matrix approach, integrable system.
Funding agency Grant number
National Natural Science Foundation of China 11875040
12126352
12126343
This project is supported by the NSF of China (grant Nos. 11875040, 12126352, and 12126343).
Received: 24.03.2022
Revised: 09.04.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 213, Issue 3, Pages 1686–1697
DOI: https://doi.org/10.1134/S0040577922120030
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik, 02.30.Ks, 05.45.Yv
MSC: 35Q51
Language: Russian
Citation: Zhihao Shi, Shangshuai Li, Da-jun Zhang, “Cauchy matrix approach to the noncommutative Kadomtsev–Petviashvili equation with self-consistent sources”, TMF, 213:3 (2022), 437–449; Theoret. and Math. Phys., 213:3 (2022), 1686–1697
Citation in format AMSBIB
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\by Zhihao~Shi, Shangshuai~Li, Da-jun~Zhang
\paper Cauchy matrix approach to the~noncommutative Kadomtsev--Petviashvili equation with self-consistent sources
\jour TMF
\yr 2022
\vol 213
\issue 3
\pages 437--449
\mathnet{http://mi.mathnet.ru/tmf10290}
\crossref{https://doi.org/10.4213/tmf10290}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538876}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022TMP...213.1686S}
\transl
\jour Theoret. and Math. Phys.
\yr 2022
\vol 213
\issue 3
\pages 1686--1697
\crossref{https://doi.org/10.1134/S0040577922120030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85144890601}
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    • This publication is cited in the following 1 articles:
    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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