Quasi-Periodic Solution and Its Asymptotic Behavior for Camassa-Holm Equation

WANG Zhen; QIN Yu-peng; ZOU Li; MA Rui-fang; ZHU Gui-xun

doi:10.3879/j.issn.1000-0887.2015.09.010

Volume 36 Issue 9

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WANG Zhen, QIN Yu-peng, ZOU Li, MA Rui-fang, ZHU Gui-xun. Quasi-Periodic Solution and Its Asymptotic Behavior for Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2015, 36(9): 990-1002. doi: 10.3879/j.issn.1000-0887.2015.09.010

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Quasi-Periodic Solution and Its Asymptotic Behavior for Camassa-Holm Equation

doi: 10.3879/j.issn.1000-0887.2015.09.010

¹School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116085, P.R.China;²School of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116085, P.R.China;³State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology), Dalian, Liaoning 116085, P.R.China

Funds: The National Natural Science Foundation of China(51379033；50921001)

Received Date: 2015-05-13
Rev Recd Date: 2015-07-08
Publish Date: 2015-09-15

Abstract

Abstract

Many researchers have paid attention to the shallow water wave model Camassa-Holm (CH) equation over the last two decades. The one-periodic solution of CH equation based on the Hirota bilinear method had been presented in our previous work. In this paper, we offer quasi-periodic solution in genus two and its asymptotic behavior. First, we have rearranged the parameters appeared in the bilinear equation system, such as the coordinate transformation, extended bilinear form and Riemman theta function and so on. Then quasi-periodic solution of CH equation is presented, which is expressed by Riemann theta function in genus two. Second, asymptotic behavior of the quasi-periodic solution is discussed. It can be shown that this solution will degenerate into its two-soliton solution.
- Camassa-Holm equation,
- bilinear form,
- quasi-periodic solution,
- Riemman theta function

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References(34)

References

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