The Two-Component Camassa–Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws
- 10.1142/S1402925112400025How to use a DOI?
- Multi-component Camassa–Holm equations; conservation laws; integrating factors
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).
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
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- 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 - 2012/11/28 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 - 10.1142/S1402925112400025 ID - Euler2012 ER -