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Hidetomo Nagai

Publications and source records attributed to Hidetomo Nagai.

9 recordsLinked to original sources
arXiv2026

Stationary Measures and Mean Flux Depending on Multiple Conserved Quantities in a Stochastic Cellular Automaton

We analyze a stochastic 5-neighbor cellular automaton with several conserved quantities, including the particle density. By examining the eigenvalue problem of the associated transition matrix, we derive an explicit formula for the stationary distribution on each irreducible component, in which the weight of each configuration is expressed in terms of the numbers of occurrences of two specific local patterns. This analysis further allows us to theoretically derive the dependence of the mean flux on the conserved quantities. In particular, we recover the mean flux formula in the deterministic case by taking the zero-noise limit of the system.

math-ph↗
arXiv2019

Discrete and Ultradiscrete Mixed Soliton Solutions

We propose a new type of soliton equation, which is obtained from the generalized discrete BKP equation. The obtained equation admits two types of soliton solutions. The signs of amplitude and velocity of the soliton solution are opposite to the other. We also propose the ultradiscrete analogues of them. The ultradiscrete equation also admits the similar properties. In particular it behaves the original Box-Ball system in a special case.

nlin.SI↗
arXiv2018

Discrete and Ultradiscrete Periodic Phase Soliton Equations

We propose new type of discrete and ultradiscrete soliton equations, which admit extended soliton solution called periodic phase soliton solution. The discrete equation is derived from the discrete DKP equation and the ultradiscrete one is obtained by applying the ultradiscrete limit. The soliton solutions have internal freedom and change their shape periodically during propagation. In particular, the ultradiscrete solution reduces into the solution to the ultradiscrete hungry Lotka-Volterra equation in a special case.

nlin.SI↗
arXiv2017

The discrete Toda equation revisited, dual $β$-Grothendieck polynomial, ultradiscretization and static soliton

This paper presents a study of the discrete Toda equation $(τ_n^t)^2+τ_{n-1}^tτ_{n+1}^t=τ_n^{t-1}τ_n^{t+1}$, that was introduced in 1977. In this paper, it has been proved that the algebraic solution of the discrete Toda equation, obtained via the Lax formalism, is naturally related to the dual Grothendieck polynomial, which is a $K$-theoretic generalization of the Schur polynomial. A tropical permanent solution to the ultradiscrete Toda equation has also been derived. The proposed method gives a tropical algebraic representation of static solitons. Lastly, a new cellular automaton realization of the ultradiscrete Toda equation has been proposed.

math-ph↗
arXiv2016

Ultradiscrete Permanent Solution to the Ultradiscrete KP Equation

We propose an ultradiscrete permanent solution to the ultradiscrete KP equation. The ultradiscrete permanent is an ultradiscrete analogue of the usual permanent. The elements on this ultradiscrete permanent solution are required some additional relations other than the ultradiscrete dispersion relation. We confirm the solution satisfying these relations and propose some explicit examples of the solution.

nlin.SI↗
arXiv2012

Tropical Krichever construction for the non-periodic box and ball system

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.

math.AG↗
arXiv2010

Ultradiscrete Plücker Relation Specialized for Soliton Solutions

We propose an ultradiscrete analogue of Plücker relation specialized for soliton solutions. It is expressed by an ultradiscrete permanent which is obtained by ultradiscretizing the permanent, that is, the signature-free determinant. Using this relation, we also show soliton solutions to the ultradiscrete KP equation and the ultradiscrete two-dimensional Toda lattice equation respectively.

nlin.SI↗
arXiv2010

Bilinear Equations and Bäcklund Transformation for Generalized Ultradiscrete Soliton Solution

Ultradiscrete soliton equations and Bäcklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between Bäcklund transformations for discrete and ultradiscrete KdV equations.

nlin.SI↗