A type of loop algebra and the associated loop algebras
A type of loop algebra and the associated loop algebras
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DOI：
10.1016/j.chaos.2006.09.031
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发表时间：
2008-07
影响因子：
7.8
通讯作者：
H. Tam;Yufeng Zhang
中科院分区：
文献类型：
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作者：
H. Tam;Yufeng Zhang
构造了一个高维扭圈代数。作为其应用，提出了一个新的Lax对，利用Tu格式，利用其相容性得到了Liouville可积的发展方程族。该层次结构的一个简化情形类似于著名的AKNS系统。其次，将扭圈代数推广到另一个高维圈代数，得到了一个具有11-势分量函数的发展方程族，其约化为标准AKNS系统.特别地，我们证明了由递推关系直接得到的四个Hamilton算子的任意线性组合仍然是Hamilton算子。因此，具有11个势函数的族具有4-Hamilton结构。最后，给出了该族的一个可积耦合。
A higher-dimensional twisted loop algebra is constructed. As its application, a new Lax pair is presented, whose compatibility gives rise to a Liouville integrable hierarchy of evolution equations by making use of Tu scheme. One of the reduction cases of the hierarchy is an analogous of the well-known AKNS system. Next, the twisted loop algebra, furthermore, is extended to another higher dimensional loop algebra, from which a hierarchy of evolution equations with 11-potential component functions is obtained, whose reduction is just standard AKNS system. Especially, we prove that an arbitrary linear combination of the four Hamiltonian operators directly obtained from the recurrence relations is still a Hamiltonian operator. Therefore, the hierarchy with 11-potential functions possesses 4-Hamiltonian structures. Finally, an integrable coupling of the hierarchy is worked out.