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.
Publisher Copyright:
© 2018 IOP Publishing Ltd.
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
SN - 1751-8113
VL - 51
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 34
M1 - 344001
ER -