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Nonlocal Symmetries and Geometric Integrability of Multi-Component Camassa–Holm and Hunter–Saxton Systems |
| YAN Lu1, SONG Jun-Feng1,2, QU Chang-Zheng1**
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1Department of Mathematics, Northwest University, Xi'an 710069
2College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
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| Cite this article: |
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YAN Lu, SONG Jun-Feng, QU Chang-Zheng 2011 Chin. Phys. Lett. 28 050204 |
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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.
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02.30.Hq
11.30.-j
02.40.Hw
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Received: 17 February 2011
Published: 26 April 2011
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| PACS: |
02.30.Hq
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(Ordinary differential equations)
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11.30.-j
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(Symmetry and conservation laws)
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02.40.Hw
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(Classical differential geometry)
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