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Symmetric Waves are Traveling Waves for the Rotation-Camassa–Holm Equation

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Abstract

In this paper, we prove that classical symmetric solutions to the rotation-Camassa–Holm equation must be traveling wave solutions. We discover how the symmetric structure is connected to the steady structure of solutions to the rotation-Camassa–Holm equation, and give a straightforward proof for symmetric waves to be traveling waves.

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Acknowledgements

This work is supported by Yunnan Fundamental Research Projects (Grant No. KKSQ202107025).

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Correspondence to Shaojie Yang.

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Communicated by A. Constantin

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Wang, T., Yang, S. & Han, X. Symmetric Waves are Traveling Waves for the Rotation-Camassa–Holm Equation. J. Math. Fluid Mech. 23, 84 (2021). https://doi.org/10.1007/s00021-021-00602-1

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