Journal of Nonlinear Mathematical Physics

Volume 24, Issue 4, September 2017, Pages 584 - 595

Liouville Integrability of Conservative Peakons for a Modified CH equation

Authors
Xiangke Chang
LSEC, Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, P.O.Box 2719, Beijing 100190, PR China
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, Canada. changxk@lsec.cc.ac.cn
Jacek Szmigielski
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, Canada. szmigiel@math.usask.ca
Received 4 May 2017, Accepted 17 June 2017, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2017.1375693How to use a DOI?
Keywords
Conservative peakons, Liouville integrability
Abstract

The modified Camassa-Holm (also called FORQ) equation is one of numerous cousins of the Camassa-Holm equation possessing non-smoth solitons (peakons) as special solutions. The peakon sector of solutions is not uniquely defined: in one peakon sector (dissipativea) the Sobolev H1 norm is not preserved, in the other sector (conservative), introduced in [2], the time evolution of peakons leaves the H1 norm invariant. In this Letter, it is shown that the conservative peakon equations of the modified Camassa-Holm can be given an appropriate Poisson structure relative to which the equations are Hamiltonian and, in fact, Liouville integrable. The latter is proved directly by exploiting the inverse spectral techniques, especially asymptotic analysis of solutions, developed elsewhere [3].

Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 4
Pages
584 - 595
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1375693How to use a DOI?
Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Xiangke Chang
AU  - Jacek Szmigielski
PY  - 2021
DA  - 2021/01
TI  - Liouville Integrability of Conservative Peakons for a Modified CH equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 584
EP  - 595
VL  - 24
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1375693
DO  - https://doi.org/10.1080/14029251.2017.1375693
ID  - Chang2021
ER  -