Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization. Zbl 1138.37341
Tokihiro, T.; Nagai, A.; Satsuma, J. |
|
1999
|
The \(A^{(1)}_M\) automata related to crystals of symmetric tensors. Zbl 1032.17021
Hatayama, G.; Hikami, K.; Inoue, R.; Kuniba, A.; Takagi, T.; Tokihiro, T. |
|
2001
|
Toda-type cellular automaton and its \(N\)-soliton solution. Zbl 0962.82526
Matsukidaira, J.; Satsuma, J.; Takahashi, D.; Tokihiro, T.; Torii, M. |
|
1997
|
The Toda molecule equation and the \(\varepsilon\)-algorithm. Zbl 0924.58028
Nagai, Atsushi; Tokihiro, Tetsuji; Satsuma, Junkichi |
|
1998
|
Darboux and binary Darboux transformations for the nonautonomous discrete KP equation. Zbl 0898.58046
Willox, R.; Tokihiro, T.; Satsuma, J. |
|
1997
|
Box and ball system as a realization of ultradiscrete nonautonomous KP equation. Zbl 0957.82023
Tokihiro, T.; Takahashi, D.; Matsukidaira, J. |
|
2000
|
Fundamental cycle of a periodic box-ball system. Zbl 1066.82036
Yoshihara, Daisuke; Yura, Fumitaka; Tokihiro, Tetsuji |
|
2003
|
Irreducibility and co-primeness as an integrability criterion for discrete equations. Zbl 1311.39009
Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji |
|
2014
|
On a periodic soliton cellular automaton. Zbl 1053.82021
Yura, Fumitaka; Tokihiro, Tetsuji |
|
2002
|
The fermionic approach to Darboux transformations. Zbl 0908.35121
Willox, R.; Tokihiro, T.; Loris, I.; Satsuma, J. |
|
1998
|
Constructing solutions to the ultradiscrete Painlevé equations. Zbl 0926.39007
Takahashi, D.; Tokihiro, T.; Grammaticos, B.; Ohta, Y.; Ramani, A. |
|
1997
|
Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring. Zbl 1106.82010
Kanai, Masahiro; Nishinari, Katsuhiro; Tokihiro, Tetsuji |
|
2006
|
From the continuous P\(_{\text{V}}\) to discrete Painlevé equations. Zbl 1046.39013
Tokihiro, T.; Grammaticos, B.; Ramani, A. |
|
2002
|
A discrete mathematical model for angiogenesis. Zbl 1352.92018
Matsuya, K.; Yura, F.; Mada, J.; Kurihara, H.; Tokihiro, T. |
|
2016
|
Ultradiscrete systems (cellular automata). Zbl 1064.37014
Tokihiro, Tetsuji |
|
2004
|
Coupled discrete KdV equations and modular genetic networks. Zbl 1309.35105
Carstea, A. S.; Tokihiro, T. |
|
2015
|
Algebraic entropy of an extended Hietarinta-Viallet equation. Zbl 1353.37131
Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2015
|
Singularity confinement and chaos in two-dimensional discrete systems. Zbl 1345.39005
Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2016
|
Discrete Painlevé II equation over finite fields. Zbl 1277.37096
Kanki, M.; Mada, J.; Tamizhmani, K. M.; Tokihiro, T. |
|
2012
|
On special function solutions to nonlinear integrable equations. Zbl 0969.33500
Tokihiro, T.; Satsuma, J.; Willox, R. |
|
1997
|
Singularities of the discrete KdV equation and the Laurent property. Zbl 1309.37059
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2014
|
Initial-value problem of the discrete periodic Toda equation and its ultradiscretization. Zbl 1021.35116
Kimijima, Taeko; Tokihiro, Tetsuji |
|
2002
|
Ultra-discrete Toda molecule equation. Zbl 1044.37549
Nagai, A.; Tokihiro, T.; Satsuma, J. |
|
1998
|
Conserved quantities and generalized solutions of the ultradiscrete KdV equation. Zbl 1217.39008
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2011
|
Two-dimensional soliton cellular automaton of deautonomized Toda-type. Zbl 1044.37502
Nagai, A.; Tokihiro, T.; Satsuma, J.; Willox, R.; Kajiwara, K. |
|
1997
|
Integrability criterion in terms of coprime property for the discrete Toda equation. Zbl 1338.37088
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2015
|
Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation. Zbl 1362.37148
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2017
|
Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow. Zbl 1522.90011
Higashi, Kohei; Satsuma, Junkichi; Tokihiro, Tetsuji |
|
2021
|
Discrete integrable equations over finite fields. Zbl 1291.35290
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2012
|
Direct ultradiscretization of Ai and Bi functions and special solutions for the Painlevé II equation. Zbl 1247.39006
Isojima, Shin; Satsuma, Junkichi; Tokihiro, Tetsuji |
|
2012
|
The box-ball system and the \(N\)-soliton solution of the ultradiscrete KdV equation. Zbl 1165.35449
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2008
|
On the initial value problem of a periodic box-ball system. Zbl 1154.37005
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2006
|
Differential equations for creating complex cellular automaton pattern. Zbl 1156.81347
Kunishima, Wataru; Nishiyama, Akinobu; Tanaka, Hiroshi; Tokihiro, Tetsuji |
|
2004
|
Modelling the morphology of migrating bacterial colonies. Zbl 1193.37135
Nishiyama, A.; Tokihiro, T.; Badoual, M.; Grammaticos, B. |
|
2010
|
Analytical study on the criticality of the stochastic optimal velocity model. Zbl 1089.82009
Kanai, Masahiro; Nishinari, Katsuhiro; Tokihiro, Tetsuji |
|
2006
|
Fundamental cycle of a periodic box-ball system and solvable lattice models. Zbl 1225.82038
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2006
|
Nonlinear forms of coprimeness preserving extensions to the Somos-4 recurrence and the two-dimensional Toda lattice equation – investigation into their extended Laurent properties. Zbl 1406.39006
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2018
|
On the coprimeness property of discrete systems without the irreducibility condition. Zbl 1393.37077
Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2018
|
Existence and non-existence of global solutions for a discrete semilinear heat equation. Zbl 1232.39009
Matsuya, Keisuke; Tokihiro, Tetsuji |
|
2011
|
Correlation functions for a periodic box-ball system. Zbl 1186.82021
Mada, Jun; Tokihiro, Tetsuji |
|
2010
|
Ultradiscretization of the theta function solution of pd Toda. Zbl 1155.37041
Iwao, Shinsuke; Tokihiro, Tetsuji |
|
2007
|
Nonautonomous discrete integrable systems. Zbl 1160.37402
Willox, R.; Tokihiro, T.; Satsuma, J. |
|
2000
|
A two-dimensional lattice equation as an extension of the Heideman-Hogan recurrence. Zbl 1388.39002
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2018
|
Conserved quantities of box and ball system. Zbl 1045.37046
Nagai, A.; Tokihiro, T.; Satsuma, J. |
|
2001
|
Path description of conserved quantities of generalized periodic box-ball systems. Zbl 1076.37009
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2005
|
Conserved quantities of generalized periodic box-ball systems constructed from ndKP equation. Zbl 1067.82044
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2004
|
The exact correspondence between conserved quantities of a periodic box-ball system and string solutions of the Bethe ansatz equations. Zbl 1111.82014
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2006
|
\(2+1\) dimensional soliton cellular automaton. Zbl 0947.68096
Moriwaki, S.; Nagai, A.; Satsuma, J.; Tokihiro, T.; Torii, M.; Takahashi, D.; Matsukidaira, J. |
|
1999
|
Solution to the initial value problem of the ultradiscrete periodic Toda equation. Zbl 1181.37096
Idzumi, Makoto; Iwao, Shinsuke; Mada, Jun; Tokihiro, Tetsuji |
|
2009
|
From cellular automaton to difference equation: a general transformation method which preserves time evolution patterns. Zbl 1059.82026
Nobe, A.; Satsuma, J.; Tokihiro, T. |
|
2001
|
Algebraic entropy of a multi-term recurrence of the Hietarinta-Viallet type. Zbl 1459.39045
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2020
|
Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow. Zbl 1522.90011
Higashi, Kohei; Satsuma, Junkichi; Tokihiro, Tetsuji |
|
2021
|
Algebraic entropy of a multi-term recurrence of the Hietarinta-Viallet type. Zbl 1459.39045
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2020
|
Nonlinear forms of coprimeness preserving extensions to the Somos-4 recurrence and the two-dimensional Toda lattice equation – investigation into their extended Laurent properties. Zbl 1406.39006
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2018
|
On the coprimeness property of discrete systems without the irreducibility condition. Zbl 1393.37077
Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2018
|
A two-dimensional lattice equation as an extension of the Heideman-Hogan recurrence. Zbl 1388.39002
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2018
|
Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation. Zbl 1362.37148
Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2017
|
A discrete mathematical model for angiogenesis. Zbl 1352.92018
Matsuya, K.; Yura, F.; Mada, J.; Kurihara, H.; Tokihiro, T. |
|
2016
|
Singularity confinement and chaos in two-dimensional discrete systems. Zbl 1345.39005
Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2016
|
Coupled discrete KdV equations and modular genetic networks. Zbl 1309.35105
Carstea, A. S.; Tokihiro, T. |
|
2015
|
Algebraic entropy of an extended Hietarinta-Viallet equation. Zbl 1353.37131
Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji |
|
2015
|
Integrability criterion in terms of coprime property for the discrete Toda equation. Zbl 1338.37088
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2015
|
Irreducibility and co-primeness as an integrability criterion for discrete equations. Zbl 1311.39009
Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji |
|
2014
|
Singularities of the discrete KdV equation and the Laurent property. Zbl 1309.37059
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2014
|
Discrete Painlevé II equation over finite fields. Zbl 1277.37096
Kanki, M.; Mada, J.; Tamizhmani, K. M.; Tokihiro, T. |
|
2012
|
Discrete integrable equations over finite fields. Zbl 1291.35290
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2012
|
Direct ultradiscretization of Ai and Bi functions and special solutions for the Painlevé II equation. Zbl 1247.39006
Isojima, Shin; Satsuma, Junkichi; Tokihiro, Tetsuji |
|
2012
|
Conserved quantities and generalized solutions of the ultradiscrete KdV equation. Zbl 1217.39008
Kanki, Masataka; Mada, Jun; Tokihiro, Tetsuji |
|
2011
|
Existence and non-existence of global solutions for a discrete semilinear heat equation. Zbl 1232.39009
Matsuya, Keisuke; Tokihiro, Tetsuji |
|
2011
|
Modelling the morphology of migrating bacterial colonies. Zbl 1193.37135
Nishiyama, A.; Tokihiro, T.; Badoual, M.; Grammaticos, B. |
|
2010
|
Correlation functions for a periodic box-ball system. Zbl 1186.82021
Mada, Jun; Tokihiro, Tetsuji |
|
2010
|
Solution to the initial value problem of the ultradiscrete periodic Toda equation. Zbl 1181.37096
Idzumi, Makoto; Iwao, Shinsuke; Mada, Jun; Tokihiro, Tetsuji |
|
2009
|
The box-ball system and the \(N\)-soliton solution of the ultradiscrete KdV equation. Zbl 1165.35449
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2008
|
Ultradiscretization of the theta function solution of pd Toda. Zbl 1155.37041
Iwao, Shinsuke; Tokihiro, Tetsuji |
|
2007
|
Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring. Zbl 1106.82010
Kanai, Masahiro; Nishinari, Katsuhiro; Tokihiro, Tetsuji |
|
2006
|
On the initial value problem of a periodic box-ball system. Zbl 1154.37005
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2006
|
Analytical study on the criticality of the stochastic optimal velocity model. Zbl 1089.82009
Kanai, Masahiro; Nishinari, Katsuhiro; Tokihiro, Tetsuji |
|
2006
|
Fundamental cycle of a periodic box-ball system and solvable lattice models. Zbl 1225.82038
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2006
|
The exact correspondence between conserved quantities of a periodic box-ball system and string solutions of the Bethe ansatz equations. Zbl 1111.82014
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2006
|
Path description of conserved quantities of generalized periodic box-ball systems. Zbl 1076.37009
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2005
|
Ultradiscrete systems (cellular automata). Zbl 1064.37014
Tokihiro, Tetsuji |
|
2004
|
Differential equations for creating complex cellular automaton pattern. Zbl 1156.81347
Kunishima, Wataru; Nishiyama, Akinobu; Tanaka, Hiroshi; Tokihiro, Tetsuji |
|
2004
|
Conserved quantities of generalized periodic box-ball systems constructed from ndKP equation. Zbl 1067.82044
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji |
|
2004
|
Fundamental cycle of a periodic box-ball system. Zbl 1066.82036
Yoshihara, Daisuke; Yura, Fumitaka; Tokihiro, Tetsuji |
|
2003
|
On a periodic soliton cellular automaton. Zbl 1053.82021
Yura, Fumitaka; Tokihiro, Tetsuji |
|
2002
|
From the continuous P\(_{\text{V}}\) to discrete Painlevé equations. Zbl 1046.39013
Tokihiro, T.; Grammaticos, B.; Ramani, A. |
|
2002
|
Initial-value problem of the discrete periodic Toda equation and its ultradiscretization. Zbl 1021.35116
Kimijima, Taeko; Tokihiro, Tetsuji |
|
2002
|
The \(A^{(1)}_M\) automata related to crystals of symmetric tensors. Zbl 1032.17021
Hatayama, G.; Hikami, K.; Inoue, R.; Kuniba, A.; Takagi, T.; Tokihiro, T. |
|
2001
|
Conserved quantities of box and ball system. Zbl 1045.37046
Nagai, A.; Tokihiro, T.; Satsuma, J. |
|
2001
|
From cellular automaton to difference equation: a general transformation method which preserves time evolution patterns. Zbl 1059.82026
Nobe, A.; Satsuma, J.; Tokihiro, T. |
|
2001
|
Box and ball system as a realization of ultradiscrete nonautonomous KP equation. Zbl 0957.82023
Tokihiro, T.; Takahashi, D.; Matsukidaira, J. |
|
2000
|
Nonautonomous discrete integrable systems. Zbl 1160.37402
Willox, R.; Tokihiro, T.; Satsuma, J. |
|
2000
|
Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization. Zbl 1138.37341
Tokihiro, T.; Nagai, A.; Satsuma, J. |
|
1999
|
\(2+1\) dimensional soliton cellular automaton. Zbl 0947.68096
Moriwaki, S.; Nagai, A.; Satsuma, J.; Tokihiro, T.; Torii, M.; Takahashi, D.; Matsukidaira, J. |
|
1999
|
The Toda molecule equation and the \(\varepsilon\)-algorithm. Zbl 0924.58028
Nagai, Atsushi; Tokihiro, Tetsuji; Satsuma, Junkichi |
|
1998
|
The fermionic approach to Darboux transformations. Zbl 0908.35121
Willox, R.; Tokihiro, T.; Loris, I.; Satsuma, J. |
|
1998
|
Ultra-discrete Toda molecule equation. Zbl 1044.37549
Nagai, A.; Tokihiro, T.; Satsuma, J. |
|
1998
|
Toda-type cellular automaton and its \(N\)-soliton solution. Zbl 0962.82526
Matsukidaira, J.; Satsuma, J.; Takahashi, D.; Tokihiro, T.; Torii, M. |
|
1997
|
Darboux and binary Darboux transformations for the nonautonomous discrete KP equation. Zbl 0898.58046
Willox, R.; Tokihiro, T.; Satsuma, J. |
|
1997
|
Constructing solutions to the ultradiscrete Painlevé equations. Zbl 0926.39007
Takahashi, D.; Tokihiro, T.; Grammaticos, B.; Ohta, Y.; Ramani, A. |
|
1997
|
On special function solutions to nonlinear integrable equations. Zbl 0969.33500
Tokihiro, T.; Satsuma, J.; Willox, R. |
|
1997
|
Two-dimensional soliton cellular automaton of deautonomized Toda-type. Zbl 1044.37502
Nagai, A.; Tokihiro, T.; Satsuma, J.; Willox, R.; Kajiwara, K. |
|
1997
|