Stability in the energy space of the sum of $N$ peakons for a Camassa-Holm-type equation with quartic nonlinearity
Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 703-728
Published online October 29, 2018
Printed May 31, 2019
Xingxing Liu
China University of Mining and Technology
Abstract : Considered herein is the orbital stability in the energy space $H^1(\R)$ of a decoupled sum of $N$ peakons for a Camassa-Holm-type equation with quartic nonlinearity, which admits single peakon and multi-peakons. Based on our obtained result of the stability of a single peakon, then combining modulation argument with monotonicity of local energy $H^1$-norm, we get the stability of the sum of $N$ peakons.
Keywords : Camassa-Holm equation, quartic nonlinearity, peakons, orbital stability
MSC numbers : 35G25, 35L05, 35Q51
Supported by : The author is supported by the Fundamental Research Funds for the Central Universities: No. 2018QNA34
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