Nonlocal Symmetries and Geometric Integrability of Multi-Component Camassa-Holm and Hunter-Saxton Systems

• 来源期刊: 中国物理快报（英文版）
• 年，卷（期）: 2011,（5）
• 页码范围: 12-15
• 页数: 4页
• 语种: 英文
• DOI: 10.1088/0256-307X/28/5/050204

摘要

We present the multi-component Hunter-Saxton and μ-Camassa-Holm systems.It is shown that the multicomponent 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.