Volume 23, Issue 4, September 2016, Pages 563 - 572
Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons
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 17 August 2016, Accepted 2 September 2016, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1248156How to use a DOI?
- Keywords
- Weak solutions; peakons; distributions
- Abstract
In this Letter we propose that for Lax integrable nonlinear partial differential equations the natural concept of weak solutions is implied by the compatibility condition for the respective distributional Lax pairs. We illustrate our proposal by comparing two concepts of weak solutions of the modified Camassa-Holm equation pointing out that in the peakon sector (a family of non-smooth solitons) only one of them, namely the one obtained from the distributional compatibility condition, supports the time invariance of the Sobolev H1 norm.
- Copyright
- © 2016 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/).
Cite this article
TY - JOUR AU - Xiangke Chang AU - Jacek Szmigielski PY - 2021 DA - 2021/01/06 TI - Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons JO - Journal of Nonlinear Mathematical Physics SP - 563 EP - 572 VL - 23 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1248156 DO - 10.1080/14029251.2016.1248156 ID - Chang2021 ER -