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,
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.
Camassa–Holm equation, bifurcation solutions, angular singularities, caustic.
PDF file (478 kB)
MSC: 34K18, 34K10
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
\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.
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