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Volume 7, Issue 3
Orbital Stability of the Sum of $N$ Peakons for the CH-mCH Equation

Dandan He, Kelei Zhang & Shengqiang Tang

DOI: 10.12150/jnma.2025.794

J. Nonl. Mod. Anal., 7 (2025), pp. 794-822.

Published online: 2025-05

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

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  • Abstract

This paper is concerned with a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities (also known as the CH-mCH equation). We mainly prove the orbital stability of the train of peakons for the CH-mCH equation in energy space, using energy arguments and combining the method of orbital stability of a single peakon with the monotonicity of the local energy norm.

  • Keywords

Camassa-Holm equation, CH-mCH equation, peakons, multi-peakons, orbital stability.

  • AMS Subject Headings

35B35, 35C08, 37K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-794, author = {He , DandanZhang , Kelei and Tang , Shengqiang}, title = {Orbital Stability of the Sum of $N$ Peakons for the CH-mCH Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {3}, pages = {794--822}, abstract = {

This paper is concerned with a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities (also known as the CH-mCH equation). We mainly prove the orbital stability of the train of peakons for the CH-mCH equation in energy space, using energy arguments and combining the method of orbital stability of a single peakon with the monotonicity of the local energy norm.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.794}, url = {http://global-sci.org/intro/article_detail/jnma/24103.html} }
TY - JOUR T1 - Orbital Stability of the Sum of $N$ Peakons for the CH-mCH Equation AU - He , Dandan AU - Zhang , Kelei AU - Tang , Shengqiang JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 794 EP - 822 PY - 2025 DA - 2025/05 SN - 7 DO - http://doi.org/10.12150/jnma.2025.794 UR - https://global-sci.org/intro/article_detail/jnma/24103.html KW - Camassa-Holm equation, CH-mCH equation, peakons, multi-peakons, orbital stability. AB -

This paper is concerned with a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities (also known as the CH-mCH equation). We mainly prove the orbital stability of the train of peakons for the CH-mCH equation in energy space, using energy arguments and combining the method of orbital stability of a single peakon with the monotonicity of the local energy norm.

He , DandanZhang , Kelei and Tang , Shengqiang. (2025). Orbital Stability of the Sum of $N$ Peakons for the CH-mCH Equation. Journal of Nonlinear Modeling and Analysis. 7 (3). 794-822. doi:10.12150/jnma.2025.794
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