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Stability of the Camassa–Holm Multi-peakons in the Dynamics of a Shallow-Water-Type System

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Abstract

Consideration herein is the stability issue of a variety of superpositions of the Camassa–Holm peakons and antipeakons in the dynamics of the two-component Camassa–Holm system, which is derived in the shallow water theory. These wave configurations accommodate the ordered trains of the Camassa–Holm peakons, the ordered trains of Camassa–Holm antipeakons and peakons as well as the Camassa–Holm multi-peakons. Using the features of conservation laws and the monotonicity properties of the local energy, we prove the orbital stability of these wave profiles in the energy space by the modulation argument.

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Acknowledgements

This paper is prepared under the guidance of my advisor, Y. Liu. The author wants to take this opportunity to express her sincere gratitude to him.

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  1. Department of Mathematics, University of Texas at Arlington, Arlington, TX, 76019-0408, USA

    Ting Luo

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  1. Ting Luo
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Correspondence to Ting Luo.

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Luo, T. Stability of the Camassa–Holm Multi-peakons in the Dynamics of a Shallow-Water-Type System. J Dyn Diff Equat 30, 1627–1659 (2018). https://doi.org/10.1007/s10884-017-9612-4

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  • DOI: https://doi.org/10.1007/s10884-017-9612-4

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