Peakons of a Generalized Camassa-Holm Equation with Bifurcation Theory of Dynamical System

Min Sun; Jing Li; Ting Ting Quan

doi:10.4028/www.scientific.net/AMM.252.36

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 252Peakons of a Generalized Camassa-Holm Equation...

Peakons of a Generalized Camassa-Holm Equation with Bifurcation Theory of Dynamical System

Abstract:

In this paper, the peakons and bifurcations in a generalized Camassa-Holm equation are studied by using the bifurcation method and qualitative theory of dynamical systems. First, the averaged equation is obtained by introducing linear transform and traveling wave transform to the generalized Camassa-Holm equation. Then, we applied the bifurcation theory of planar dynamical system and maple software to investigate the averaged equation. The phase portrait of the system under a parameter condition is obtained. Finally, we get the peakons from the limit of general single solitary wave solution.

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Periodical:

Applied Mechanics and Materials (Volume 252)

Pages:

36-39

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.252.36

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Online since:

December 2012

Authors:

Min Sun, Jing Li, Ting Ting Quan

Keywords:

Bifurcation, Camassa-Holm Equation, Dynamical System, Transform of Traveling Wave

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References

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