Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations
Bi-Hamiltonian systems on the dual of the Lie algebra of vector fields of the circle and periodic shallow water equations
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DOI：
10.1098/rsta.2007.2012
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发表时间：
2006-09
期刊：
影响因子：
--
通讯作者：
B. Kolev
中科院分区：
文献类型：
--
作者：
B. Kolev
本文是关于圆上向量场李代数对偶上的双Hamilton系统的综述。在这里，我们研究的特殊情况下，其中一个结构是典型的李泊松结构和第二个是常数。这些结构，称为仿射或修改的李-泊松结构，涉及到某些欧拉方程的可积性，作为浅水波的模型。
This paper is a survey article on bi-Hamiltonian systems on the dual of the Lie algebra of vector fields on the circle. Here, we investigate the special case where one of the structures is the canonical Lie–Poisson structure and the second one is constant. These structures, called affine or modified Lie–Poisson structures, are involved in the integrability of certain Euler equations that arise as models for shallow water waves.