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Equations with Peakon Solutions in the Negative Order Camassa-Holm Hierarchy
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-02-28
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
The negative order Camassa-Holm (CH) hierarchy consists of nonlinear evolution equations associated with the CH spectral problem.
In this paper, we show that all the negative order CH equations admit peakon solutions; the Lax pair of the N-order CH equation given by the hierarchy is compatible with its peakon solutions.
Special peakon-antipeakon solutions for equations of orders -3 and -4 are obtained.
Indeed, for N≤-2, the peakons of N-order CH equation can be constructed explicitly by the inverse scattering approach using Stieltjes continued fractions.
The properties of peakons for N-order CH equation when N is odd are much different from the CH peakons; we present the case N=-3 as an example.
American Psychological Association (APA)
Dong, Fengfeng& Zhou, Lingjun. 2018. Equations with Peakon Solutions in the Negative Order Camassa-Holm Hierarchy. Advances in Mathematical Physics،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1119078
Modern Language Association (MLA)
Dong, Fengfeng& Zhou, Lingjun. Equations with Peakon Solutions in the Negative Order Camassa-Holm Hierarchy. Advances in Mathematical Physics No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1119078
American Medical Association (AMA)
Dong, Fengfeng& Zhou, Lingjun. Equations with Peakon Solutions in the Negative Order Camassa-Holm Hierarchy. Advances in Mathematical Physics. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1119078
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119078