# NOBE Atsushi

Last updated: Dec 10, 2019 at 18:52

Name NOBE Atsushi Chiba University Faculty of Education, Mathematics Education Associate Professor 80397728 0000-0002-5520-5519

## Research Areas

2004
-
2007
Research Associate, Graduate School of Engineering Science, Osaka University

2007

-　Assistant Professor, Graduate School of Engineering Science, Osaka University

## Committee Memberships

2008

The Physical Society of Japan

## Published Papers

NOBE Atsushi, MATSUKIDAIRA Junta
RIMS Kokyuroku Bessatsu      Sep 2019   [Refereed]
The one-parameter family of second order nonlinear difference equations each
of which is given by x_{n-1}x_nx_{n+1}=x_{n-1}+(x_n)^{\beta-1}+x_{n+1}
\qquad(\beta\in\mathbb{N}) is explored. Since the equation above is arising
from seed mutatio...
NOBE Atsushi
Journal of Mathematical Physics   60    Aug 2019   [Refereed]
From the viewpoint of integrable systems on algebraic curves, we discuss
linearization of birational maps arising from the seed mutations of types
and , which enables us to construct the set of all
cluster variables generati...
NOBE Atsushi
Jan 2018
Mutations of the cluster variables generating the cluster algebra of type
reduce to a two-dimensional discrete integrable system given by a
quartic birational map. The invariant curve of the map is a singular quartic
curve, and its res...
NOBE Atsushi
Japan Journal of Industrial and Applied Mathematics   33(3) 537-556   Dec 2016   [Refereed]
NOBE Atsushi
Journal of Physics A: Mathematical and Theoretical   49(28)    Jul 2016   [Refereed]
NOBE Atsushi
RIMS Kokyuroku   1765 188-208   Dec 2011
We give the addition formula for the tropical Hesse pencil, which is the
tropicalization of the Hesse pencil parametrized by the level-three theta
theta functions are re...
NOBE Atsushi
RIMS Kokyuroku Bessatsu   B47 55-76   Dec 2014   [Refereed]
This is a review article on a tropical geometric realization of the
ultradiscrete periodic Toda lattice (UD-pTL). Time evolution of the UD-pTL is
translated into an addition on the Picard group of its spectral curve, which is
a tropical hyperellip...
NOBE Atsushi
Journal of Physics A: Mathematical and Theoretical   46(46)    Nov 2013   [Refereed]
Addition in Jacobians of hyperelliptic curves and the periodic discrete Toda lattice
NOBE Atsushi
RIAM Report   No.23AO-S7 84-89   Mar 2012   [Refereed]
NOBE Atsushi
RIMS Kokyuroku Bessatsu   B30 25-51   Nov 2012   [Refereed]
We show that there exists a surjection from the set of effective divisors of
degree on a tropical curve of genus to its Jacobian by using a tropical
version of the Riemann-Roch theorem. We then show that the restriction of the
surjection i...
Nobe Atsushi
PHYSICS LETTERS A   375(47) 4178-4182   Nov 2011   [Refereed]
Atsushi Nobe
RIAM Report No.22AO-S8 (2011) 37-42      Apr 2011
We investigate a tropical analogue of the Hessian group , the group
of linear automorphisms acting on the Hesse pencil. Through the procedure of
ultradiscretization, the group law on the Hesse pencil reduces to that on the
tropical Hesse ...
Kenji Kajiwara, Masanobu Kaneko, Atsushi Nobe, Teruhisa Tsuda
Kyushu Journal of Mathematics   63(2) 315-338   Oct 2009   [Refereed]
We present a solvable two-dimensional piecewise linear chaotic map that arises from the duplication map of a certain tropical cubic curve. Its general solution is constructed by means of the ultradiscrete theta function. We show that the map is de...
Atsushi Nobe
Journal of Physics A: Mathematical and Theoretical   41(12)    Mar 2008   [Refereed]
It is shown that the polygonal invariant curve of the ultradiscrete QRT (uQRT) map, which is a two-dimensional piecewise linear integrable map, is the complement of the tentacles of a tropical elliptic curve on which the curve has a group structur...
Kenji Kajiwara, Atsushi Nobe, Teruhisa Tsuda
Journal of Physics A: Mathematical and Theoretical   41(39)    Mar 2008   [Refereed]
We consider the ultradiscretization of a solvable one-dimensional chaotic map
which arises from the duplication formula of the elliptic functions. It is
shown that ultradiscrete limit of the map and its solution yield the tent map
and its solution...
NOBE Atsushi, YURA Fumitaka
Journal of Physics A: Mathematical and Theoretical   40(26) 7159-7174   Jun 2007   [Refereed]
ISOJIMA Shin, MURATA Mikio, NOBE Atsushi, SATSUMA Junkichi
Physics Letters, Section A: General, Atomic and Solid State Physics   357(1) 31-35   Aug 2006   [Refereed]
The discrete modified Korteweg-de Vries equation admits exact solutions with nondefinite sign, which describe interaction among solitons with positive and negative amplitude. In this Letter a transformation of hyperbolic sine type is proposed in o...
NOBE Atsushi
Journal of Physics A: Mathematical and General   39(20) 335-342   May 2006   [Refereed]
It is shown that there exist three kinds of ultradiscrete analogues of Jacobi's elliptic functions. In this process, the asymptotic behaviour of the poles and the zeros of the functions plays a crucial role. Using the ultradiscrete analogues and a...
MURATA Mikio, ISOJIMA Shin, NOBE Atsushi, SATSUMA Junkichi
Journal of Physics A: Mathematical and General   39(1) 27-34   Jan 2006   [Refereed]
A new class of solutions is proposed for discrete and ultradiscrete modified KdV equations. These are directly related to solutions of the box and ball system with a carrier. Moreover, an extended box and ball system and its exact solutions are di...
NOBE Atsushi
Journal of Physics A: Mathematical and General   38(43) 715-723   Oct 2005   [Refereed]
An ultradiscretization of the Riemann theta function is proposed. The ultradiscretization satisfies an addition formula, which is an ultradiscrete analogue of an addition formula for the Riemann theta function. Using the addition formula, periodic...
ISOJIMA Shin, MURATA Mikio, NOBE Atsushi, SATSUMA Junkichi
Physics Letters, Section A: General, Atomic and Solid State Physics   331(6) 378-386   Nov 2004   [Refereed]
An ultradiscrete system corresponding to the sine-Gordon equation is proposed. A new dependent variable for the discrete sine-Gordon equation is introduced in order to apply the procedure of ultradiscretization. The ultradiscrete system possesses ...
NOBE Atsushi, YURA Fumitaka
Journal of Physics A: Mathematical and General   37(22) 5789-5804   Jun 2004   [Refereed]
Reversibility of one-dimensional cellular automata with periodic boundary conditions is discussed. It is shown that there exist exactly 16 reversible elementary cellular automaton rules for infinitely many cell sizes by means of a correspondence b...
NOBE Atsushi
Theoretical and Applied Mechanics Japan   52 229-237   Dec 2003   [Refereed]
An eight-parameter family of two-dimensional piecewise linear mappings is discussed. Since the dynamical system is obtained from the QRT system through the ultradiscretization, the dynamical system is called the ultradiscrete QRT system. The ultra...
Stable dynamical systems associated with cellular automata
Doctoral thesis, Univ. of Tokyo      2002
NOBE Atsushi, SATSUMA Junkichi, TOKIHIRO Tetsuji
Journal of Physics A: Mathematical and General   34(25) 371-379   Dec 2001   [Refereed]
We propose a general method to construct a partial difference equation which preserves any time evolution patterns of a cellular automaton. The method is based on inverse ultradiscretization with filter functions. © 2001 IOP Publishing Ltd.
ATSUSHI NOBE, JUNKICHI Satsuma, TOKIHIRO Tetsuji
Japan Journal of Industrial and Applied Mathematics   18 No.2 (2001) 293-305 293-305   Jan 2001   [Refereed]
We construct a difference equation which preserves any time evolution pattern of the rule 90 elementary cellular automaton. We also demonstrate that such difference equations can be obtained for any elementary cellular automata.
KOSHIZUKA Seiichi, NOBE Atsushi, OKA Yoshiaki
International Journal for Numerical Methods in Fluids   26(7) 751-769   Apr 1998   [Refereed]
The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-i...

## Misc

Atsushi Nobe
Journal of Mathematical Physics 60, 072702 (2019)      Aug 2018
From the viewpoint of integrable systems on algebraic curves, we discuss
linearization of birational maps arising from the seed mutations of types
and , which enables us to construct the set of all
cluster variables generati...

## Conference Activities & Talks

A family of integrable and non-integrable difference equations arising from cluster algebras [Invited]
NOBE Atsushi
Cluster Algebras 2019   20 Jun 2019
Chaos in cluster algebras [Invited]
NOBE Atsushi
5 Sep 2018

Mutations of cluster algebras and discrete integrable systems [Invited]
NOBE Atsushi
The Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory   29 Mar 2017
Tropical elliptic curves and discrete integrable systems [Invited]
NOBE Atsushi
Workshop on Tropical geometry - basic and applications   21 Jan 2017

Ultradiscretization of generalized Toda lattices [Invited]
NOBE Atsushi
Workshop on Integrable and nonintegrable lattice models: theory and computation   16 Jul 2016

A geometric realization of the periodic discrete Toda lattice and its tropicalization
NOBE Atsushi
China-Japan Joint Workshop on Integrable Systems 2013   19 Mar 2013
Integrable maps arising from the addition on tropical elliptic curves [Invited]
NOBE Atsushi
Mini-Workshop: Tropical geometry and ultradiscrete integrable systems, NEEDS 2012   10 Jul 2012
Tropical Jacobian of a hyperelliptic curve [Invited]
NOBE Atsushi
International Workshop on Tropical and Quantum Geometries   14 Feb 2012

KAJIWARA Kenji, NOBE Atsushi, TSUDA Teruhisa

Tropical curves, integrable maps and solvable chaos [Invited]
NOBE Atsushi
Workshop Crystals and Tropical Combinatorics''   27 Aug 2008
NOBE Atsushi
NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan   2003

Stable difference equations associated with elementary cellular automata
NOBE Atsushi, SATSUMA Junkichi, TOKIHIRO Tetsuji
4th International Interdisciplinary Meeting on Symmetries and Integrability of Difference Equations (SIDE4)"   30 Nov 2000
SATSUMA Junkichi, TOKIHIRO Tetsuji, NOBE Atsushi
Meeting Abstracts of the Physical Society of Japan   1998
NOBE A., SATSUMA J., TOKIHIRO T., OHTA Y.
Meeting Abstracts of the Physical Society of Japan   1998

## Works

Tropical geometry and integrable systems
2007