TY - JOUR
T1 - Ultradiscrete Lotka-Volterra system computes tropical eigenvalue of symmetric tridiagonal matrices
AU - Fukuda, Akiko
AU - Watanabe, Sennosuke
AU - Hanaoka, Ayumi
AU - Iwasaki, Masashi
N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.
PY - 2019/5/31
Y1 - 2019/5/31
N2 - Some of authors' recent study shows that the time evolution of the integrable ultradiscrete Toda equation computes eigenvalue of tridiagonal matrices over min-plus algebra, where min-plus algebra is a semiring with two binary operations: ⊕ : = min and ⊗ : = +. In this paper, we rst present a Backlund transformation between the ultradiscrete Toda equation and the ultradiscrete Lotka-Volterra system. Using the Backlund transformation, we show that the ultradiscrete Lotka-Volterra system can also compute eigenvalue of symmetric tridiagonal matrices over min-plus algebra.
AB - Some of authors' recent study shows that the time evolution of the integrable ultradiscrete Toda equation computes eigenvalue of tridiagonal matrices over min-plus algebra, where min-plus algebra is a semiring with two binary operations: ⊕ : = min and ⊗ : = +. In this paper, we rst present a Backlund transformation between the ultradiscrete Toda equation and the ultradiscrete Lotka-Volterra system. Using the Backlund transformation, we show that the ultradiscrete Lotka-Volterra system can also compute eigenvalue of symmetric tridiagonal matrices over min-plus algebra.
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U2 - 10.1088/1742-6596/1218/1/012015
DO - 10.1088/1742-6596/1218/1/012015
M3 - Conference article
AN - SCOPUS:85067798328
SN - 1742-6588
VL - 1218
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012015
T2 - 3rd International Conference on Mathematics; Pure, Applied and Computation, ICoMPAC 2018
Y2 - 20 October 2018
ER -