Volume 25, Issue 2, March 2018, Pages 290 - 308
Inverse Spectral Problem and Peakons of an Integrable Two-component Camassa-Holm System
Authors
Fengfeng Dong
School of Mathematical Sciences, Tongji University, Shanghai 200092, P.R. China,1433494@tongji.edu.cn
Lingjun Zhou
School of Mathematical Sciences, Tongji University, Shanghai 200092, P.R. China,zhoulj@tongji.edu.cn
Received 19 November 2017, Accepted 17 December 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2018.1452674How to use a DOI?
- Keywords
- peakon; two-component Camassa-Holm system; continued fractions; inverse spectral approach
- Abstract
In this paper, we are concerned with the explicit construction of peakon solutions of the integrable twocomponent system with cubic non-linearity. We establish the spectral and inverse spectral problem associated to the Lax pairs of the system. The inverse problem is solved by the classical results of Stieltjes continued fractions, which also contributes a lot to the spectral problem. The explicit formulas are obtained from solutions of the inverse problem. The positivity of the spectral measures is implied by J. Moser's work on the Jacobi spectral problem.
- Copyright
- © 2018 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Download article (PDF)
View full text (HTML)
Cite this article
TY - JOUR AU - Fengfeng Dong AU - Lingjun Zhou PY - 2021 DA - 2021/01/06 TI - Inverse Spectral Problem and Peakons of an Integrable Two-component Camassa-Holm System JO - Journal of Nonlinear Mathematical Physics SP - 290 EP - 308 VL - 25 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2018.1452674 DO - 10.1080/14029251.2018.1452674 ID - Dong2021 ER -