Volume 4, Issue 1
Stability of Peakons for a Nonlinear Generalization of the Camassa-Holm Equation

Hao Yu & Kelei Zhang

J. Nonl. Mod. Anal., 4 (2022), pp. 141-152.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • AMS Subject Headings

34C25, 34C60, 37C27, 37C75

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COPYRIGHT: © Global Science Press

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@Article{JNMA-4-141, author = {Yu , Hao and Zhang , Kelei}, title = {Stability of Peakons for a Nonlinear Generalization of the Camassa-Holm Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {1}, pages = {141--152}, abstract = {

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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.141}, url = {http://global-sci.org/intro/article_detail/jnma/20699.html} }
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 -

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.

Yu , Hao and Zhang , Kelei. (2022). Stability of Peakons for a Nonlinear Generalization of the Camassa-Holm Equation. Journal of Nonlinear Modeling and Analysis. 4 (1). 141-152. doi:10.12150/jnma.2022.141
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