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Equations with Peakon Solutions in the Negative Order Camassa-Holm Hierarchy

Dong, Fengfeng ; Zhou, Lingjun Mironov, Andrei D.

Advances in Mathematical Physics, 2018-01, Vol.2018, p.1-11 [Peer Reviewed Journal]

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Title:
Equations with Peakon Solutions in the Negative Order Camassa-Holm Hierarchy
Author: Dong, Fengfeng ; Zhou, Lingjun
Mironov, Andrei D.
Subjects: Analysis ; Peakons ; Scattering theory
Is Part Of: Advances in Mathematical Physics, 2018-01, Vol.2018, p.1-11
Description: 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.
Publisher: Hindawi
Language: English

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