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

Please always quote using this URN: urn:nbn:de:0297-zib-16087
  • 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).

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Author:Marianna Euler, Norbert Euler, Thomas Wolf
Document Type:ZIB-Report
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX)
Date of first Publication:2012/10/16
Series (Serial Number):ZIB-Report (12-30)
ISSN:1438-0064
Published in:To appear in: Journal of Nonlinear Mathematical Physics