TY - GEN A1 - Euler, Marianna A1 - Euler, Norbert A1 - Wolf, Thomas T1 - The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws N2 - Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations 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, {\it J. Phys A: Math. Theor} {\bf 43}, 492001 (20pp), 2010]. 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 sent 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). T3 - ZIB-Report - 12-30 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16087 SN - 1438-0064 ER - TY - JOUR A1 - Euler, Marianna A1 - Euler, Norbert A1 - Wolf, Thomas T1 - The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws JF - Journal of Nonlinear Mathematical Physics N2 - 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). Y1 - 2013 U6 - https://doi.org/10.1142/S1402925112400025 VL - 19 IS - 1 SP - 13 EP - 22 ER -