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Criterion for Lyapunov stability of periodic Camassa–Holm equations

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Abstract

We study the Lyapunov stability of the periodic Camassa–Holm equation in terms of the periodic/anti-periodic eigenvalues and the associated spectral intervals. We consider the case with definite potentials as well as the case with indefinite potentials. In particular, we prove a Lyapunov-type stability criterion.

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Authors and Affiliations

  1. Department of Mathematics, Nan**g University of Aeronautics and Astronautics, Nan**g, 210016, China

    Feng Cao

  2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nan**g, 211106, China

    Feng Cao

  3. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Jifeng Chu

  4. School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, China

    Ke Jiang

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  1. Feng Cao
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  2. Jifeng Chu
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  3. Ke Jiang
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Correspondence to Jifeng Chu.

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Feng Cao was supported by the National Natural Science Foundation of China (Grant No. 11871273). Jifeng Chu was supported by the National Natural Science Foundation of China (Grant No. 12071296) and by Science and Technology Innovation Plan of Shanghai (Grant No. 20JC1414200).

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Cao, F., Chu, J. & Jiang, K. Criterion for Lyapunov stability of periodic Camassa–Holm equations. Annali di Matematica 202, 1557–1572 (2023). https://doi.org/10.1007/s10231-022-01292-w

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  • DOI: https://doi.org/10.1007/s10231-022-01292-w

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