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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 219, Number 1, Pages 124–150
DOI: https://doi.org/10.4213/tmf10427 (Mi tmf10427) 		 
Classification of the two-component Benjamin–Ono systems

Min Zhao, Changzheng Qu

School of Mathematics and Statistics, Ningbo University, Ningbo, China
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DOI: https://doi.org/10.4213/tmf10427
Abstract: The Benjamin–Ono equation involving the Hilbert transformation has been studied extensively from different standpoints. Its variant forms and multi-component extensions have been proposed. In this paper, we study the classification of two-component Benjamin–Ono-type systems of the general form. Our classification is carried out by developing the perturbative symmetry approach due to Mikhailov and Novikov. As a result, new two-component integrable Benjamin–Ono type systems are obtained.
Keywords: Benjamin–Ono equation, symmetry, perturbative symmetry approach, two-component Benjamin–Ono system, recursion operator.
Funding agency Grant number
National Natural Science Foundation of China 11971251
11631007
12111530003
K. C. Wong Magna Fund (Ningbo University)
The work of Min Zhao is supported by the National Science Foundation of China (grant No. 11971251) and K. C. Wong Magna Fund in Ningbo University. The work of Changzheng Qu is supported by the National Science Foundation of China (grant Nos. 11971251, 11631007, and 12111530003).
Received: 09.12.2022
Revised: 01.09.2023
English version:
Theoretical and Mathematical Physics, 2024, Volume 219, Issue 1, Pages 638–662
DOI: https://doi.org/10.1134/S0040577924040093
Bibliographic databases:
Document Type: Article
MSC: 37K06, 37K10, 35B06.
Language: Russian
Citation: Min Zhao, Changzheng Qu, “Classification of the two-component Benjamin–Ono systems”, TMF, 219:1 (2024), 124–150; Theoret. and Math. Phys., 219:1 (2024), 638–662
Citation in format AMSBIB
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\by Min~Zhao, Changzheng~Qu
\paper Classification of the~two-component Benjamin--Ono systems
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\pages 124--150
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\jour Theoret. and Math. Phys.
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\vol 219
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\pages 638--662
\crossref{https://doi.org/10.1134/S0040577924040093}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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