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Blow-up for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions

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Abstract

This paper is devoted to an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions. We present a precise blow-up scenario and a new blow-up result for strong solutions to the system. However, due to higher-order nonlinearity, the estimate of several required nonlinear terms is very hard. A complicated problem is that we deal with the equation with higher-order nonlinearity, making the proof of several required nonlinear estimates some what delicate.

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Acknowledgements

The work of Mi is partially supported by NSF of Chongqing (cstc2020jcyj-jqX0025). The work of Huang is partially supported by NSF of China (11971067, 11631008, 11771183).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Yangtze Normal University, Chongqing, 408100, People’s Republic of China

    Yongsheng Mi

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, People’s Republic of China

    Daiwen Huang

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  1. Yongsheng Mi
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  2. Daiwen Huang
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Correspondence to Yongsheng Mi.

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Communicated by Joachim Escher.

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Mi, Y., Huang, D. Blow-up for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions. Monatsh Math 198, 153–164 (2022). https://doi.org/10.1007/s00605-021-01635-4

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