A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations
A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations
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DOI：
10.1088/0305-4470/37/4/018
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发表时间：
2004-01
期刊：
影响因子：
--
通讯作者：
W. Ma;Xi-Xiang Xu
中科院分区：
文献类型：
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作者：
W. Ma;Xi-Xiang Xu
从一个修正的户田谱问题出发，通过离散的零曲率方程，构造了一族具有两个任意常数的广义户田格点方程.证明了该族具有双Hamilton结构和遗传递归算子，这意味着存在无穷多个公共交换对称和无穷多个公共交换守恒泛函.两种情况下所涉及的常数提出了两个特定的可积子族，其中之一正是户田格族。
Starting from a modified Toda spectral problem, a hierarchy of generalized Toda lattice equations with two arbitrary constants is constructed through discrete zero curvature equations. It is shown that the hierarchy possesses a bi-Hamiltonian structure and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals. Two cases of the involved constants present two specific integrable sub-hierarchies, one of which is exactly the Toda lattice hierarchy.