Non-isospectral lattice hierarchies in 2 1 dimensions and generalized discrete Painleve hierarchies

作者:Gordoa, PR*; Pickering, A; Zhu, ZN
来源:Journal of Nonlinear Mathematical Physics, 2005, 12: 180-196.
DOI:10.2991/jnmp.2005.12.s2.13

摘要

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 Painleve hierarchy which includes as special cases, after further summation, both the standard discrete first Painleve hierarchy and a new extended version of the discrete thirty-fourth Painleve hierarchy.