A Three-component Extension of the Camassa–Holm Hierarchy

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• 作者：Laura Fontanelli ; Paolo Lorenzoni and Marco Pedroni
• 关键词：Integrable hierarchies of PDEs ; Camassa–Holm equation ; bi ; Hamiltonian manifolds ; Marsden–Ratiu reduction
• 刊名：Letters in Mathematical Physics
• 出版年：2006
• 出版时间：November, 2006
• 年：2006
• 卷：78
• 期：2
• 页码：125-137
• 全文大小：148 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Statistical Physics
  Geometry
  Group Theory and Generalizations
  
• 出版者：Springer Netherlands
• ISSN：1573-0530

文摘

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of\mathfraksl(2)\mathfrak{sl}(2) endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation.