Periodic convergence in the discrete hungry Toda equation
Periodic convergence in the discrete hungry Toda equation
复制标题
离散饥饿 Toda 方程的周期性收敛
DOI：
10.1088/1751-8121/aaccb5
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发表时间：
2018
影响因子：
2.1
通讯作者：
Yoshimasa Nakamura
中科院分区：
文献类型：
--
作者：
You Takahashi;Masashi Iwasaki;Akiko Fukuda;Emiko Ishiwata;Yoshimasa Nakamura
本文阐明了离散饥饿Toda方程（dhToda）的周期性质，该方程是著名的可积离散Toda方程的推广。中心流形理论作为一种经典的分析理论，在分析dhToda方程中起着关键作用。我们首先通过一个数值例子观察了dhToda变量的渐近行为。然后讨论了与dhToda方程相关的中心流形的存在性。最后，我们找到了这个中心流形，然后分析了离散时间变量趋于无穷时dhToda变量的渐近行为。
In this paper, we clarify the periodic behaviour in the discrete hungry Toda (dhToda) equation, which is an extension of the famous integrable discrete Toda equation. The centre manifold theory, which is a classical analysis theory, plays a key role in analysing the dhToda equation. We first observe the asymptotic behaviour of the dhToda variable through a numerical example. We then discuss the existence of a centre manifold associated with the dhToda equation. Finally, we find this centre manifold and then analyse the asymptotic behaviour of the dhToda variable as the discrete-time variable goes to infinity.