Non-isospectral lattice hierarchies in 2+1 dimensions and generalized discrete Painlevé hierarchies
Non-isospectral lattice hierarchies in 2+1 dimensions and generalized discrete Painlevé hierarchies
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DOI：
10.2991/jnmp.2005.12.s2.13
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发表时间：
2005-01
影响因子：
0.7
通讯作者：
P. R. Gordoa;A. Pickering;Z. N. Zhu
中科院分区：
文献类型：
--
作者：
P. R. Gordoa;A. Pickering;Z. N. Zhu
摘要在最近的一篇论文中，我们介绍了一个新的2 + 1维非等谱扩展的沃尔泰拉晶格的层次，沿着其相应的层次的基本线性问题。在这里，我们考虑减少这个格层次的离散方程，我们再次获得沿着与他们的层次的基本线性问题。我们获得了一个广义离散第一Painlevé层次结构，在进一步求和后，它包括标准离散第一Painlevé层次结构和离散第三十四Painlevé层次结构的新扩展版本作为特殊情况。
Abstract In a recent paper we introduced a new 2 + 1-dimensional non-isospectral extension of the Volterra lattice hierarchy, along with its corresponding hierarchy of underlying linear problems. Here we consider reductions of this lattice hierarchy to hierarchies of discrete equations, which we obtain once again along with their hierarchy of underlying linear problems. We obtain a generalized discrete first Painlevé hierarchy which includes as special cases, after further summation, both the standard discrete first Painlevé hierarchy and a new extended version of the discrete thirty-fourth Painlevé hierarchy.