Periodic convergence in the discrete hungry Toda equation. (16th July 2018)

• Record Type: Journal Article
• Authors: Takahashi, You; Iwasaki, Masashi; Fukuda, Akiko; Ishiwata, Emiko; Nakamura, Yoshimasa
• Is Part Of: Journal of physics. Volume 51:Number 34(2018)
• Publication Date: 2018-07-16
• Subjects: centre manifold -- discrete hungry Toda equation -- local analysis -- periodic convergence; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aaccb5
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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.