A generalized AKNS hierarchy and its bi-Hamiltonian structures
A generalized AKNS hierarchy and its bi-Hamiltonian structures
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DOI：
10.1016/j.chaos.2004.07.004
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发表时间：
2005-03
影响因子：
7.8
通讯作者：
T. Xia;Fucai You;Dengyuan Chen
中科院分区：
文献类型：
--
作者：
T. Xia;Fucai You;Dengyuan Chen
首先，我们在本文中构建了一个具有 8 个势的新等谱问题。然后出现了新的 Lax 对。利用Tu格式推导了一类新的孤子层次方程，该方程在Liouville意义上可积，并且具有双哈密顿结构。经过一些简化，得到了众所周知的AKNS层次结构和其他层次结构的演化方程。最后，为了说明本文得到的孤子层次完全具有双哈密尔顿结构，我们不断地证明了承认的双哈密尔顿算子的线性组合也是哈密尔顿算子。我们指出系统获得的两个哈密顿算子是直接从递推关系推导出来的，而不是从递推算子推导出来的。
First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator.