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Probl. Anal. Issues Anal., 2020, Volume 9(27), Issue 1, Pages 66–82 (Mi pa289)  

The analysis of bifurcation solutions of the Camassa–Holm equation by angular singularities

H. K. Kadhim, M. A. Abdul Hussain

Faculty of Education for Pure Sciences, Department of Mathematics, University of Basrah, Basrah, Iraq

Abstract: This paper studies bifurcation solutions of the Camassa–Holm equation by using the local Lyapunov–Schmidt method. The Camassa–Holm equation is studied by reduction to an ODE. We find the key function that corresponds to the functional related to this equation and defined on a new domain. The bifurcation analysis of the key function is investigated by the angular singularities. We find the parametric equation of the bifurcation set (caustic) with its geometric description. Also, the bifurcation spreading of the critical points is found.

Keywords: Camassa–Holm equation, bifurcation solutions, angular singularities, caustic.

DOI: https://doi.org/10.15393/j3.art.2020.6770

Full text: PDF file (478 kB)
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Bibliographic databases:

UDC: 517.968, 517.988
MSC: 34K18, 34K10
Received: 22.07.2019
Revised: 21.01.2020
Accepted:26.01.2020
Language:

Citation: H. K. Kadhim, M. A. Abdul Hussain, “The analysis of bifurcation solutions of the Camassa–Holm equation by angular singularities”, Probl. Anal. Issues Anal., 9(27):1 (2020), 66–82

Citation in format AMSBIB
\Bibitem{KadAbd20}
\by H.~K.~Kadhim, M.~A.~Abdul Hussain
\paper The analysis of bifurcation solutions of the Camassa--Holm equation by angular singularities
\jour Probl. Anal. Issues Anal.
\yr 2020
\vol 9(27)
\issue 1
\pages 66--82
\mathnet{http://mi.mathnet.ru/pa289}
\crossref{https://doi.org/10.15393/j3.art.2020.6770}
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\elib{https://elibrary.ru/item.asp?id=43711307}


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