Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2019; 56(3): 703-728

Online first article October 29, 2018      Printed May 31, 2019

https://doi.org/10.4134/BKMS.b180512

Copyright © The Korean Mathematical Society.

Stability in the energy space of the sum of $N$ peakons for a Camassa-Holm-type equation with quartic nonlinearity

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