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

Fengfeng Dong and Lingjun Zhou

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: 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.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2018/1679625

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:1679625

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().