Soliton cellular automaton, Toda molecule equation and sorting algorithm

Nagai, Atsushi; Takahashi, Daisuke; Tokihiro, Tetsuji

doi:10.1016/s0375-9601(99)00162-0

Cited by 38 publications

(39 citation statements)

References 10 publications

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“…It is worth pointing out here that the time evolution of the (e i , f i ) is known to satisfy the ultradiscrete Toda molecule equation with boundary condition f 0 = f N = ∞ [14].…”

Section: The Solitons and Backgroundmentioning

confidence: 99%

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A direct approach to the ultradiscrete KdV equation with negative and non-integer site values

Gilson

Nimmo

Nagai

2015

J. Phys. A: Math. Theor.

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“…It is worth pointing out here that the time evolution of the (e i , f i ) is known to satisfy the ultradiscrete Toda molecule equation with boundary condition f 0 = f N = ∞ [14].…”

Section: The Solitons and Backgroundmentioning

confidence: 99%

“…One of the simplest, which we shall describe here is due to Nagai et al [14,4]. Firstly, though, we shall write down our initial solution with the background removed.…”

Section: The Solitonsmentioning

confidence: 99%

A direct approach to the ultradiscrete KdV equation with negative and non-integer site values

Gilson

Nimmo

Nagai

2015

J. Phys. A: Math. Theor.

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show abstract

“…There are two types of evolution equations for the BBS. One is derived from the discrete KdV lattice which corresponds to the Euler representation and another is from the discrete Toda lattice with finite boundary condition [3] which corresponds to the "difference form" of the Lagrange representation, we call the finite Toda representation in this paper. Note that these Euler-Lagrange notions for cellular automata come from hydrodynamics [4].…”

Section: Introductionmentioning

confidence: 99%

Another generalization of the box–ball system with many kinds of balls

Maeda

2018

Journal of Integrable Systems

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A cellular automaton that is a generalization of the box-ball system with either many kinds of balls or finite carrier capacity is proposed and studied through two discrete integrable systems: nonautonomous discrete KP lattice and nonautonomous discrete two-dimensional Toda lattice. Applying reduction technique and ultradiscretization procedure to these discrete systems, we derive two types of time evolution equations of the proposed cellular automaton, and particular solutions to the ultradiscrete equations.

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“…Recently, the researche areas using ultradiscritizations is extending and it contains crystal formulations, combinatorics, stochastic cellular automata and algorithms [1,2,4,5].…”

Section: Introductionmentioning

confidence: 99%

The Number of Orbits of Periodic Box-Ball Systems

Mikoda

Inokuchi

Mizoguchi

et al. 2006

Lecture Notes in Computer Science

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Abstract.A box-ball system is a kind of cellular automata obtained by the ultradiscrete Lotka-Volterra equation. Similarities and differences between behavious of discrete systems (cellular automata) and continuous systems (differential equations) are investigated using techniques of ultradiscretizations. Our motivations is to take advantage of behavious of box-ball systems for new kinds of computations. Especially, we tried to find out useful periodic box-ball systems(pBBS) for random number generations. Applicable pBBS systems should have long fundamental cycles. We focus on pBBS with at most two kinds of solitons and investigate their behaviours, especially, the length of cycles and the number of orbits. We showed some relational equations of soliton sizes, a box size and the number of orbits. Varying a box size, we also found out some simulation results of the periodicity of orbits of pBBS with same kinds of solitons.

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Soliton cellular automaton, Toda molecule equation and sorting algorithm

Cited by 38 publications

References 10 publications

A direct approach to the ultradiscrete KdV equation with negative and non-integer site values

A direct approach to the ultradiscrete KdV equation with negative and non-integer site values

Another generalization of the box–ball system with many kinds of balls

The Number of Orbits of Periodic Box-Ball Systems

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