TY - JOUR
T1 - Stability of Peakons for a Nonlinear Generalization of the Camassa-Holm Equation
AU - Yu , Hao
AU - Zhang , Kelei
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 141
EP - 152
PY - 2022
DA - 2022/06
SN - 4
DO - http://doi.org/10.12150/jnma.2022.141
UR - https://global-sci.org/intro/article_detail/jnma/20699.html
KW - Camassa-Holm equation, Peakon, Stability, Heteroclinic cycle,
Orbital stability.
AB - <p style="text-align: justify;">In this paper, by using the dynamic system method and the known
conservation laws of the gCH equation, and underlying features of the peakons,
we study the peakon solutions and the orbital stability of the peakons for
a nonlinear generalization of the Camassa-Holm equation (gCH). The gCH
equation is first transformed into a planar system. Then, by the first integral
and algebraic curves of this system, we obtain one heteroclinic cycle, which
corresponds to a peakon solution. Moreover, we give a proof of the orbital
stability of the peakons for the gCH equation.</p>