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Volume 2, Issue 3
New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation

Xinhui Lu, Lin Lu & Aiyong Chen

DOI: 10.12150/jnma.2020.345

J. Nonl. Mod. Anal., 2 (2020), pp. 345-353.

Published online: 2021-04

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

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  • Abstract

In this paper, we obtain new peakon and periodic peakon solutions to a modified Camassa-Holm equation. We change the modified Camassa-Holm equation into a planar system. Then the first integral and algebraic curves of this system are obtained. By using the first integral and algebraic curves, a new peakon solution is given by hyperbolic function. Moreover, some new periodic peakons are given by elliptic functions and triangle functions.

  • Keywords

Camassa-Holm equation, Peakon, Periodic peakon, Solitary wave, Periodic wave.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-2-345, author = {Lu , XinhuiLu , Lin and Chen , Aiyong}, title = {New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {2}, number = {3}, pages = {345--353}, abstract = {

In this paper, we obtain new peakon and periodic peakon solutions to a modified Camassa-Holm equation. We change the modified Camassa-Holm equation into a planar system. Then the first integral and algebraic curves of this system are obtained. By using the first integral and algebraic curves, a new peakon solution is given by hyperbolic function. Moreover, some new periodic peakons are given by elliptic functions and triangle functions.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.345}, url = {http://global-sci.org/intro/article_detail/jnma/18815.html} }
TY - JOUR T1 - New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation AU - Lu , Xinhui AU - Lu , Lin AU - Chen , Aiyong JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 345 EP - 353 PY - 2021 DA - 2021/04 SN - 2 DO - http://doi.org/10.12150/jnma.2020.345 UR - https://global-sci.org/intro/article_detail/jnma/18815.html KW - Camassa-Holm equation, Peakon, Periodic peakon, Solitary wave, Periodic wave. AB -

In this paper, we obtain new peakon and periodic peakon solutions to a modified Camassa-Holm equation. We change the modified Camassa-Holm equation into a planar system. Then the first integral and algebraic curves of this system are obtained. By using the first integral and algebraic curves, a new peakon solution is given by hyperbolic function. Moreover, some new periodic peakons are given by elliptic functions and triangle functions.

Lu , XinhuiLu , Lin and Chen , Aiyong. (2021). New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation. Journal of Nonlinear Modeling and Analysis. 2 (3). 345-353. doi:10.12150/jnma.2020.345
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