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Wave-breaking and persistence properties in weighted \(L^p\) spaces for a Camassa–Holm type equation with quadratic and cubic nonlinearities

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Abstract

We consider the Cauchy problem of a Camassa–Holm type equation with quadratic and cubic nonlinearities. We establish a new sufficient condition on the initial data that leads to the wave-breaking for this equation. Moreover, we obtain the persistence results of solutions for the equation in weighted \(L^p\) spaces.

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Acknowledgements

The work of Cheng is partially supported by the National Natural Science Foundation of China (Nos. 12201417 and 12381240294), and the Project funded by China Postdoctoral Science Foundation (No. 2023M733173). The work of Lin is partially supported by the National Natural Science Foundation of China (No. 12375006).

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Authors and Affiliations

  1. Department of Mathematics, Shaoxing University, Shaoxing, 312000, Zhejiang, China

    Wenguang Cheng

  2. Department of Physics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wenguang Cheng & Ji Lin

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  1. Wenguang Cheng
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  2. Ji Lin
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Correspondence to Ji Lin.

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Communicated by Adrian Constantin.

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Cheng, W., Lin, J. Wave-breaking and persistence properties in weighted \(L^p\) spaces for a Camassa–Holm type equation with quadratic and cubic nonlinearities. Monatsh Math (2024). https://doi.org/10.1007/s00605-023-01938-8

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