A look on some results about Camassa–Holm type equations

Igor Leite Freire

doi:10.2478/cm-2021-0006

Igor Leite Freire - A look on some results about Camassa–Holm type equations

cm:9525 - Communications in Mathematics, April 30, 2021, Volume 29 (2021), Issue 1 (Special Issue: Ostrava Mathematical Seminar) - https://doi.org/10.2478/cm-2021-0006

A look on some results about Camassa–Holm type equationsArticle

Authors: Igor Leite Freire

We present an overview of some contributions of the author regarding Camassa–Holm type equations. We show that an equation unifying both Camassa–Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.

https://doi.org/10.2478/cm-2021-0006

Source: HAL:hal-03665012v1

Volume: Volume 29 (2021), Issue 1 (Special Issue: Ostrava Mathematical Seminar)

Published on: April 30, 2021

Imported on: May 11, 2022

Keywords: [MATH]Mathematics [math]

Licence: Attribution-Non Commercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

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Mathematics Subject Classification 2020¹

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[1] zbMATH Open.

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Review available on zbMATH Open, by Jipeng Cheng (Xuzhou) (English)

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Bibliographic References

10 Documents citing this article

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Nilay Duruk Mutlubas;Igor Leite Freire, 2022, The Cauchy problem and continuation of periodic solutions for a generalized Camassa–Holm equation, arXiv (Cornell University), 102, 12, pp. 3209-3222, 10.1080/00036811.2022.2057304, http://arxiv.org/abs/2202.07110.

Priscila Leal da Silva;Igor Leite Freire, 2022, Existence, persistence, and continuation of solutions for a generalized 0-Holm-Staley equation, arXiv (Cornell University), 320, pp. 371-398, 10.1016/j.jde.2022.02.058, http://arxiv.org/abs/2008.11848.

Sen Ming;Jiayi Du;Yaxian Ma, 2022, The Cauchy problem for coupled system of the generalized Camassa-Holm equations, AIMS Mathematics, 7, 8, pp. 14738-14755, 10.3934/math.2022810, https://doi.org/10.3934/math.2022810.

Shaoyong Lai;Kexin Luo, 2022, Wave breaking to a shallow water wave equation involving the Fornberg-Whitham model, Journal of Differential Equations, 344, pp. 509-521, 10.1016/j.jde.2022.11.006.

Yarema Prykarpatskyy;Myroslava Vovk;Petro Pukach, 2022, Operator-valued Camassa–Holm systems and their integrability, Letters in Mathematical Physics, 112, 4, 10.1007/s11005-022-01566-7, https://doi.org/10.1007/s11005-022-01566-7.

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