Journal of Nonlinear Mathematical Physics

Volume 19, Issue Supplement 1, March 2013, Pages 13 - 22

The Two-Component Camassa–Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws

Authors
Marianna Euler*, Norbert Euler
Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
Thomas Wolf
Department of Mathematics, Brock University, 500 Glenridge Avenue, St. Catharines, Ontario, Canada L2S 3A1, Canada, twolf@brocku.ca
Corresponding Author
Marianna Euler
Received 3 April 2012, Accepted 8 August 2012, Available Online 28 November 2012.
DOI
https://doi.org/10.1142/S1402925112400025How to use a DOI?
Keywords
Multi-component Camassa–Holm equations, conservation laws, integrating factors
Abstract

Recently, Holm and Ivanov, proposed and studied a class of multi-component generalizations of the Camassa–Holm equations [D. D. Holm and R. I. Ivanov, Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples, J. Phys A: Math. Theor.43 (2010) 492001 (20pp)]. We consider two of those systems, denoted by Holm and Ivanov by CH(2,1) and CH(2,2), and report a class of integrating factors and its corresponding conservation laws for these two systems. In particular, we obtain the complete set of first-order integrating factors for the systems in Cauchy–Kovalevskaya form and evaluate the corresponding sets of conservation laws for CH(2,1) and CH(2,2).

Copyright
© 2012 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
19 - Supplement 1
Pages
13 - 22
Publication Date
2012/11
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925112400025How to use a DOI?
Copyright
© 2012 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  - Marianna Euler
AU  - Norbert Euler
AU  - Thomas Wolf
PY  - 2012
DA  - 2012/11
TI  - The Two-Component Camassa–Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws
JO  - Journal of Nonlinear Mathematical Physics
SP  - 13
EP  - 22
VL  - 19
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112400025
DO  - https://doi.org/10.1142/S1402925112400025
ID  - Euler2012
ER  -