The (2+1)-dimensional nonisospectral relativistic Toda hierarchy related to the generalized discrete Painlevé hierarchy
The (2+1)-dimensional nonisospectral relativistic Toda hierarchy related to the generalized discrete Painlevé hierarchy
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DOI：
10.1088/1751-8113/40/27/019
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发表时间：
2007-06
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通讯作者：
Zuo-nong Zhu
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作者：
Zuo-nong Zhu
在这篇文章中，我们将集中讨论2+1维中的可积离散族，以及它们与离散Painlevé族的联系。通过考虑一个（2+1）维非等谱离散线性问题，构造了两个新的（2+1）维非等谱可积格族：2+1非等谱相对论户田格族和2+1非等谱负相对论户田格族.结果表明，这两个新的2+1非等谱格族的约化导致（2+1）维非等谱沃尔泰拉格族和（2+1）维非等谱负沃尔泰拉格族.我们还得到了两个新的（1+1）维非等谱可积格族和两个新的常差格族，它们是这两个2+1非等谱可积格族的直接约化.两个差分层次之一产生我们先前获得的广义离散第一Painlevé（dPI）层次和另一个产生一个广义替代离散第二Painlevé（alt-dPII）层次。
In this paper, we will concentrate on the topic of integrable discrete hierarchies in 2+1 dimensions, and their connection with discrete Painlevé hierarchies. By considering a (2+1)-dimensional nonisospectral discrete linear problem, two new (2+1)-dimensional nonisospectral integrable lattice hierarchies—the 2+1 nonisospectral relativistic Toda lattice hierarchy and the 2+1 nonisospectral negative relativistic Toda lattice hierarchy—are constructed. It is shown that the reductions of the two new 2+1 nonisospectral lattice hierarchies lead to the (2+1)-dimensional nonisospectral Volterra lattice hierarchy and the (2+1)-dimensional nonisospectral negative Volterra lattice hierarchy. We also obtain two new (1+1)-dimensional nonisospectral integrable lattice hierarchies and two new ordinary difference hierarchies which are direct reductions of the two 2+1 nonisospectral integrable lattice hierarchies. One of the two difference hierarchies yields our previously obtained generalized discrete first Painlevé (dPI) hierarchy and another one yields a generalized alternative discrete second Painlevé (alt-dPII) hierarchy.