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
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
摘要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.
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.
YAN Lu;SONG Jun-Feng;QU Chang-Zheng**
. Nonlocal Symmetries and Geometric Integrability of Multi-Component Camassa–Holm and Hunter–Saxton Systems[J]. 中国物理快报, 2011, 28(5): 50204-050204.
YAN Lu, SONG Jun-Feng, QU Chang-Zheng**
. Nonlocal Symmetries and Geometric Integrability of Multi-Component Camassa–Holm and Hunter–Saxton Systems. Chin. Phys. Lett., 2011, 28(5): 50204-050204.
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