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Volume 16, Issue 2, June 2009, Pages 117 - 125
A Note on Traveling Wave Solutions to the Two Component Camassa–Holm Equation
Authors
Keivan Mohajer
Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada,mohajer@math.usask.ca
Received 12 June 2008, Accepted 2 September 2008, Available Online 7 January 2021.
- DOI
- 10.1142/S140292510900011XHow to use a DOI?
- Keywords
- Camassa–Holm equation; traveling waves; peakons
- Abstract
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa–Holm equation are distributional traveling wave solutions to the Camassa–Holm equation provided that the set u-1(c), where c is the speed of the wave, is of measure zero. In particular there are no new peakon or cuspon solutions beyond those already satisfying the Camassa–Holm equation. However, the two component Camassa–Holm equation has distinct from Camassa–Holm equation smooth traveling wave solutions as well as new distributional solutions when the measure of u-1(c) is not zero. We provide examples of such solutions.
- Copyright
- © 2009 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 - Keivan Mohajer PY - 2021 DA - 2021/01/07 TI - A Note on Traveling Wave Solutions to the Two Component Camassa–Holm Equation JO - Journal of Nonlinear Mathematical Physics SP - 117 EP - 125 VL - 16 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1142/S140292510900011X DO - 10.1142/S140292510900011X ID - Mohajer2021 ER -