Journal of Nonlinear Mathematical Physics

Volume 22, Issue 1, December 2014, Pages 1 - 16

New solutions with peakon creation in the Camassa–Holm and Novikov equations

Authors
Marcus Kardell
Department of Mathematics, Linköping University, Linköping, 581 83, Sweden. marcus.kardell@liu.se
Received 28 May 2014, Accepted 9 September 2014, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2015.996435How to use a DOI?
Keywords
Novikov, Camassa–Holm, peakon, weak solution
Abstract

In this article we study a new kind of unbounded solutions to the Novikov equation, found via a Lie symmetry analysis. These solutions exhibit peakon creation, i.e., these solutions are smooth up until a certain finite time, at which a peak is created. We show that the functions are still weak solutions for those times where the peak lives. We also find similar unbounded solutions with peakon creation in the related Camassa–Holm equation, by making an ansatz inspired by the Novikov solutions. Finally, we see that the same ansatz for the Degasperis–Procesi equation yields unbounded solutions where a peakon is present for all times.

Copyright
© 2015 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)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
22 - 1
Pages
1 - 16
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2015.996435How to use a DOI?
Copyright
© 2015 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  - Marcus Kardell
PY  - 2021
DA  - 2021/01/06
TI  - New solutions with peakon creation in the Camassa–Holm and Novikov equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 16
VL  - 22
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.996435
DO  - https://doi.org/10.1080/14029251.2015.996435
ID  - Kardell2021
ER  -