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A look on some results about Camassa–Holm type equations

A look on some results about Camassa–Holm type equations AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics de Gruyter

A look on some results about Camassa–Holm type equations

Freire, Igor Leite
Communications in Mathematics , Volume 29 (1): 16 – Jun 1, 2021
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Publisher
de Gruyter
Copyright
© 2021 Igor Leite Freire, published by Sciendo
eISSN
2336-1298
DOI
10.2478/cm-2021-0006
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Communications in Mathematics – de Gruyter

Published: Jun 1, 2021

Keywords: Invariance; Sobolev norm; peakon solutions; Camassa–Holm equation; Novikov equation; 37K40; 35Q51

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