Journal of Nonlinear Mathematical Physics

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
https://doi.org/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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 2
Pages
117 - 125
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S140292510900011XHow to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - Keivan Mohajer
PY  - 2021
DA  - 2021/01
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  - https://doi.org/10.1142/S140292510900011X
ID  - Mohajer2021
ER  -