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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
- 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/).
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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 - 10.1080/14029251.2015.996435 ID - Kardell2021 ER -