Geodesic
Classification of the~two-component Benjamin--Ono systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 124-150

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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.
Mots-clés : Benjamin–Ono equation
Keywords: symmetry, perturbative symmetry approach, two-component Benjamin–Ono system, recursion operator. 
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     author = {Min Zhao and Changzheng Qu},
     title = {Classification of the~two-component {Benjamin--Ono} systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a8/}
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Min Zhao; Changzheng Qu. Classification of the~two-component Benjamin--Ono systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 124-150. http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a8/