This article is cited in 3 papers

Classification of the two-component Benjamin–Ono systems

Min Zhao, Changzheng Qu

School of Mathematics and Statistics, Ningbo University, Ningbo, China

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.

MSC: 37K06, 37K10, 35B06.

Received: 09.12.2022
Revised: 01.09.2023

DOI: 10.4213/tmf10427

 English version: Theoretical and Mathematical Physics, 2024, 219:1, 638–662

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