TY - JOUR

T1 - Periodic convergence in the discrete hungry Toda equation

AU - Takahashi, You

AU - Iwasaki, Masashi

AU - Fukuda, Akiko

AU - Ishiwata, Emiko

AU - Nakamura, Yoshimasa

N1 - Funding Information:
The authors thank the reviewers for their careful reading and helpful comments. This work was partially supported by Grant-in-Aid for Young Scientists (B) No. 16K21368 from the Japan Society for the Promotion of Science.

PY - 2018/7/16

Y1 - 2018/7/16

N2 - 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.

AB - 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.

KW - centre manifold

KW - discrete hungry Toda equation

KW - local analysis

KW - periodic convergence

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U2 - 10.1088/1751-8121/aaccb5

DO - 10.1088/1751-8121/aaccb5

M3 - Article

AN - SCOPUS:85050484802

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 34

M1 - 344001

ER -