Chin. Phys. Lett.  2011, Vol. 28 Issue (5): 050204    DOI: 10.1088/0256-307X/28/5/050204
GENERAL |
Nonlocal Symmetries and Geometric Integrability of Multi-Component Camassa–Holm and Hunter–Saxton Systems
YAN Lu1, SONG Jun-Feng1,2, QU Chang-Zheng1**
1Department of Mathematics, Northwest University, Xi'an 710069
2College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
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Abstract We present the multi-component Hunter–Saxton and μ−Camassa–Holm systems. It is shown that the multi-component Camassa–Holm, Hunter–Saxton and μ-Camassa–Holm systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws can be directly constructed. For the three-component Camassa–Holm and Hunter–Saxton systems, their nonlocal symmetries depending on the pseudo-potentials are obtained.
Keywords: 02.30.Hq      11.30.-j      02.40.Hw     
Received: 17 February 2011      Published: 26 April 2011
PACS:  02.30.Hq (Ordinary differential equations)  
  11.30.-j (Symmetry and conservation laws)  
  02.40.Hw (Classical differential geometry)  
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YAN Lu, SONG Jun-Feng, QU Chang-Zheng 2011 Chin. Phys. Lett. 28 050204
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http://cpl.iphy.ac.cn/10.1088/0256-307X/28/5/050204       OR      http://cpl.iphy.ac.cn/Y2011/V28/I5/050204
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YAN Lu
SONG Jun-Feng
QU Chang-Zheng
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