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On the integrability of some two-component Camassa–Holm-type systems

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Abstract

Some two-component Camassa–Holm-type systems are proposed. These systems are shown to be integrable with Lax pairs and bi-Hamiltonian structures. We construct dual hierarchies of these two-component Camassa–Holm-type systems via the tri-Hamiltonian duality method, and derive spectral problems of these dual hierarchies.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant Nos 11747010 and 11805071) and the Initial Founding of Scientific Research for the introduction of talents of Huaqiao University (Project No. 16BS513).

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Authors and Affiliations

  1. School of Mathematics, Huaqiao University, Quanzhou, 362021, Fujian, People’s Republic of China

    Hongmin Li & Xiaoyong Li

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  1. Hongmin Li
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  2. Xiaoyong Li
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Correspondence to Hongmin Li.

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Li, H., Li, X. On the integrability of some two-component Camassa–Holm-type systems. Pramana - J Phys 92, 65 (2019). https://doi.org/10.1007/s12043-019-1725-3

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  • DOI: https://doi.org/10.1007/s12043-019-1725-3

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