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Hirota, Ryogo

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Author ID: hirota.ryogo Recent zbMATH articles by "Hirota, Ryogo"
Published as: Hirota, Ryogo; Hirota, R.; Hirota, Ryōgo
External Links: Wikidata · GND
Documents Indexed: 61 Publications since 1960, including 1 Book

Publications by Year

Citations contained in zbMATH Open

48 Publications have been cited 2,131 times in 1,664 Documents Cited by Year
Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons. Zbl 1168.35423
Hirota, Ryogo
678
1971
The direct method in soliton theory. Translated from the 1992 Japanese original and edited by Atsushi Nagai, Jon Nimmo and Claire Gilson. Zbl 1099.35111
Hirota, Ryogo
257
2004
Exact envelope-soliton solutions of a nonlinear wave equation. Zbl 0257.35052
Hirota, Ryogo
215
1973
A new form of Bäcklund transformations and its relation to the inverse scattering problem. Zbl 1168.37322
Hirota, Ryogo
117
1974
Exact N-soliton solutions of the wave equations of long waves in shallow- water and in nonlinear lattices. Zbl 0261.76008
Hirota, Ryogo
111
1973
\(N\)-soliton solutions of model equations for shallow water waves. Zbl 1334.76016
Hirota, Ryogo; Satsuma, Junkichi
97
1976
Nonlinear partial difference equations. I: A difference analogue of the Korteweg-de Vries equation. Zbl 1334.39013
Hirota, Ryogo
61
1977
Theory of solid state plasma waveguide in a transverse magnetic field. Zbl 0124.21603
Hirota, R.
56
1964
Hierarchies of coupled soliton equations. I. Zbl 1160.37395
Hirota, Ryogo; Ohta, Yasuhiro
52
1991
Nonlinear partial difference equations. III: Discrete sine-Gordon equation. Zbl 1334.39015
Hirota, Ryogo
48
1977
Nonlinear partial difference equations. II: Discrete-time Toda equation. Zbl 1334.39014
Hirota, Ryogo
40
1977
Nonlinear evolution equations generated from the Bäcklund transformation for the Boussinesq equation. Zbl 1098.81547
Hirota, Ryogo; Satsuma, Junkichi
34
1977
A vector potential KdV equation and vector Ito equation: Soliton solutions, bilinear Bäcklund transformations and Lax pairs. Zbl 1055.35100
Hirota, Ryogo; Hu, Xing-Biao; Tang, Xiao-Yan
30
2003
Casorati and discrete Gram type determinant representations of solutions to the discrete KP hierarchy. Zbl 0972.37536
Ohta, Yasuhiro; Hirota, Ryogo; Tsujimoto, Satoshi; Imai, Tatsuya
28
1993
Direct method of finding exact solutions of nonlinear evolution equations. Zbl 0336.35024
Hirota, Ryogo
27
1976
How to find the conserved quantities of nonlinear discrete equations. Zbl 0998.39010
Hirota, Ryogo; Kimura, Kinji; Yahagi, Hideyuki
23
2001
Discretization of the Euler top. Zbl 1058.70504
Hirota, Ryogo; Kimura, Kinji
21
2000
Soliton solutions of a coupled modified KdV equations. Zbl 0946.35078
Iwao, Masataka; Hirota, Ryogo
21
1997
Conserved quantities of a class of nonlinear difference-difference equations. Zbl 0972.39501
Hirota, Ryogo; Tsujimoto, Satoshi
21
1995
Soliton structure of the Drinfel’d-Sokolov-Wilson equation. Zbl 0638.35071
Hirota, R.; Grammaticos, B.; Ramani, A.
20
1986
Discretization of the Lagrange top. Zbl 1058.70506
Kimura, Kinji; Hirota, Ryogo
16
2000
Pfaffian representation of solutions to the discrete BKP hierarchy in bilinear form. Zbl 0948.39007
Tsujimoto, Satoshi; Hirota, Ryogo
16
1996
A new class of integrable discrete systems. Zbl 1042.37012
Kimura, K.; Yahagi, H.; Hirota, R.; Ramani, A.; Grammaticos, B.; Ohta, Y.
13
2002
Difference scheme of soliton equations. Zbl 0900.35332
Hirota, Ryogo; Tsujimoto, Satoshi; Imai, Tatsuya
13
1993
Nonlinear evolution equations generated from the Bäcklund transformation for the Toda lattice. Zbl 1079.35536
Hirota, Ryogo; Satsuma, Junkichi
12
1976
Time-discretization of soliton equations. Zbl 0961.35135
Hirota, Ryogo; Iwao, Masataka
11
2000
Second modified KdV equation and its exact multisoliton solution. Zbl 1334.35292
Nakamura, Akira; Hirota, Ryogo
9
1980
Conserved quantities of “random-time Toda equation”. Zbl 0942.82014
Hirota, Ryogo
9
1997
Nonlinear partial difference equations. IV: Bäcklund transformations for the discrete-time Toda equation. Zbl 1334.39016
Hirota, Ryogo
8
1978
The Bäcklund and inverse scattering transform of the K-dV equation with nonuniformities. Zbl 1334.81103
Hirota, Ryogo
8
1979
Pfaffian and determinant solutions to a discretized Toda equation for \(B_r\), \(C_r\) and \(D_r\). Zbl 0914.39001
Kuniba, Atsuo; Nakamura, Shuichi; Hirota, Ryogo
7
1996
Ultradiscrete KdV equation. Zbl 0948.39008
Tsujimoto, Satoshi; Hirota, Ryogo
7
1998
“Molecule solutions” of coupled modified KdV equations. Zbl 0944.35074
Hirota, Ryogo
7
1997
Reduction of soliton equations in bilinear form. Zbl 0601.35099
Hirota, Ryogo
6
1986
Soliton equations exhibiting Pfaffian solutions. Zbl 0986.35093
Hirota, Ryogo; Iwao, Masataka; Tsujimoto, Satoshi
6
2001
Discretization of coupled modified KdV equations. Zbl 1115.37345
Hirota, Ryogo
4
2000
Soliton solutions of a coupled derivative modified KdV equations. Zbl 0967.35122
Iwao, Masataka; Hirota, Ryogo
3
2000
Discretization of the potential modified KdV equation. Zbl 0946.35081
Hirota, Ryogo
3
1998
The Bäcklund transformation equations for the ultradiscrete KP equation. Zbl 1052.37056
Shinzawa, Nobuhiko; Hirota, Ryogo
3
2003
Discretization of coupled soliton equations. Zbl 1131.35382
Hirota, Ryogo
3
2006
Discretization of the new type of soliton equations. Zbl 1223.35276
Hirota, Ryogo; Ohta, Yasuhiro
2
2007
New solutions to the ultradiscrete soliton equations. Zbl 1173.39005
Hirota, Ryogo
2
2009
Ultradiscretization of the Tzitzeica equation. Zbl 1076.37065
Hirota, Ryogo; Takahashi, Daisuke
1
2005
“Recurrence equations”, an integrable system. Zbl 1065.39034
Hirota, Ryogo; Yahagi, Hideyuki
1
2002
Addition formula for Pfaffians. Zbl 1301.39003
Hirota, Ryogo
1
2013
Bilinear forms of soliton equations. Zbl 0539.70027
Hirota, Ryogo
1
1983
Multi-component generalizations of four integrable differential-difference equations: soliton solutions and bilinear Bäcklund transformations. Zbl 1066.35104
Zhao, Jun-Xiao; Hu, Xing-Biao; Hirota, Ryogo
1
2004
Ultradiscrete analogue of the identity of Pfaffians. Zbl 1236.39009
Hirota, Ryogo
1
2009
Addition formula for Pfaffians. Zbl 1301.39003
Hirota, Ryogo
1
2013
New solutions to the ultradiscrete soliton equations. Zbl 1173.39005
Hirota, Ryogo
2
2009
Ultradiscrete analogue of the identity of Pfaffians. Zbl 1236.39009
Hirota, Ryogo
1
2009
Discretization of the new type of soliton equations. Zbl 1223.35276
Hirota, Ryogo; Ohta, Yasuhiro
2
2007
Discretization of coupled soliton equations. Zbl 1131.35382
Hirota, Ryogo
3
2006
Ultradiscretization of the Tzitzeica equation. Zbl 1076.37065
Hirota, Ryogo; Takahashi, Daisuke
1
2005
The direct method in soliton theory. Translated from the 1992 Japanese original and edited by Atsushi Nagai, Jon Nimmo and Claire Gilson. Zbl 1099.35111
Hirota, Ryogo
257
2004
Multi-component generalizations of four integrable differential-difference equations: soliton solutions and bilinear Bäcklund transformations. Zbl 1066.35104
Zhao, Jun-Xiao; Hu, Xing-Biao; Hirota, Ryogo
1
2004
A vector potential KdV equation and vector Ito equation: Soliton solutions, bilinear Bäcklund transformations and Lax pairs. Zbl 1055.35100
Hirota, Ryogo; Hu, Xing-Biao; Tang, Xiao-Yan
30
2003
The Bäcklund transformation equations for the ultradiscrete KP equation. Zbl 1052.37056
Shinzawa, Nobuhiko; Hirota, Ryogo
3
2003
A new class of integrable discrete systems. Zbl 1042.37012
Kimura, K.; Yahagi, H.; Hirota, R.; Ramani, A.; Grammaticos, B.; Ohta, Y.
13
2002
“Recurrence equations”, an integrable system. Zbl 1065.39034
Hirota, Ryogo; Yahagi, Hideyuki
1
2002
How to find the conserved quantities of nonlinear discrete equations. Zbl 0998.39010
Hirota, Ryogo; Kimura, Kinji; Yahagi, Hideyuki
23
2001
Soliton equations exhibiting Pfaffian solutions. Zbl 0986.35093
Hirota, Ryogo; Iwao, Masataka; Tsujimoto, Satoshi
6
2001
Discretization of the Euler top. Zbl 1058.70504
Hirota, Ryogo; Kimura, Kinji
21
2000
Discretization of the Lagrange top. Zbl 1058.70506
Kimura, Kinji; Hirota, Ryogo
16
2000
Time-discretization of soliton equations. Zbl 0961.35135
Hirota, Ryogo; Iwao, Masataka
11
2000
Discretization of coupled modified KdV equations. Zbl 1115.37345
Hirota, Ryogo
4
2000
Soliton solutions of a coupled derivative modified KdV equations. Zbl 0967.35122
Iwao, Masataka; Hirota, Ryogo
3
2000
Ultradiscrete KdV equation. Zbl 0948.39008
Tsujimoto, Satoshi; Hirota, Ryogo
7
1998
Discretization of the potential modified KdV equation. Zbl 0946.35081
Hirota, Ryogo
3
1998
Soliton solutions of a coupled modified KdV equations. Zbl 0946.35078
Iwao, Masataka; Hirota, Ryogo
21
1997
Conserved quantities of “random-time Toda equation”. Zbl 0942.82014
Hirota, Ryogo
9
1997
“Molecule solutions” of coupled modified KdV equations. Zbl 0944.35074
Hirota, Ryogo
7
1997
Pfaffian representation of solutions to the discrete BKP hierarchy in bilinear form. Zbl 0948.39007
Tsujimoto, Satoshi; Hirota, Ryogo
16
1996
Pfaffian and determinant solutions to a discretized Toda equation for \(B_r\), \(C_r\) and \(D_r\). Zbl 0914.39001
Kuniba, Atsuo; Nakamura, Shuichi; Hirota, Ryogo
7
1996
Conserved quantities of a class of nonlinear difference-difference equations. Zbl 0972.39501
Hirota, Ryogo; Tsujimoto, Satoshi
21
1995
Casorati and discrete Gram type determinant representations of solutions to the discrete KP hierarchy. Zbl 0972.37536
Ohta, Yasuhiro; Hirota, Ryogo; Tsujimoto, Satoshi; Imai, Tatsuya
28
1993
Difference scheme of soliton equations. Zbl 0900.35332
Hirota, Ryogo; Tsujimoto, Satoshi; Imai, Tatsuya
13
1993
Hierarchies of coupled soliton equations. I. Zbl 1160.37395
Hirota, Ryogo; Ohta, Yasuhiro
52
1991
Soliton structure of the Drinfel’d-Sokolov-Wilson equation. Zbl 0638.35071
Hirota, R.; Grammaticos, B.; Ramani, A.
20
1986
Reduction of soliton equations in bilinear form. Zbl 0601.35099
Hirota, Ryogo
6
1986
Bilinear forms of soliton equations. Zbl 0539.70027
Hirota, Ryogo
1
1983
Second modified KdV equation and its exact multisoliton solution. Zbl 1334.35292
Nakamura, Akira; Hirota, Ryogo
9
1980
The Bäcklund and inverse scattering transform of the K-dV equation with nonuniformities. Zbl 1334.81103
Hirota, Ryogo
8
1979
Nonlinear partial difference equations. IV: Bäcklund transformations for the discrete-time Toda equation. Zbl 1334.39016
Hirota, Ryogo
8
1978
Nonlinear partial difference equations. I: A difference analogue of the Korteweg-de Vries equation. Zbl 1334.39013
Hirota, Ryogo
61
1977
Nonlinear partial difference equations. III: Discrete sine-Gordon equation. Zbl 1334.39015
Hirota, Ryogo
48
1977
Nonlinear partial difference equations. II: Discrete-time Toda equation. Zbl 1334.39014
Hirota, Ryogo
40
1977
Nonlinear evolution equations generated from the Bäcklund transformation for the Boussinesq equation. Zbl 1098.81547
Hirota, Ryogo; Satsuma, Junkichi
34
1977
\(N\)-soliton solutions of model equations for shallow water waves. Zbl 1334.76016
Hirota, Ryogo; Satsuma, Junkichi
97
1976
Direct method of finding exact solutions of nonlinear evolution equations. Zbl 0336.35024
Hirota, Ryogo
27
1976
Nonlinear evolution equations generated from the Bäcklund transformation for the Toda lattice. Zbl 1079.35536
Hirota, Ryogo; Satsuma, Junkichi
12
1976
A new form of Bäcklund transformations and its relation to the inverse scattering problem. Zbl 1168.37322
Hirota, Ryogo
117
1974
Exact envelope-soliton solutions of a nonlinear wave equation. Zbl 0257.35052
Hirota, Ryogo
215
1973
Exact N-soliton solutions of the wave equations of long waves in shallow- water and in nonlinear lattices. Zbl 0261.76008
Hirota, Ryogo
111
1973
Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons. Zbl 1168.35423
Hirota, Ryogo
678
1971
Theory of solid state plasma waveguide in a transverse magnetic field. Zbl 0124.21603
Hirota, R.
56
1964
all top 5

Cited by 1,736 Authors

80 Wazwaz, Abdul-Majid Abdul-Rahman
57 Tian, Bo
38 Ma, Wen-Xiu
33 Hu, Xingbiao
27 Liu, Wenjun J.
27 Zhang, Dajun
24 Zhang, Sheng
22 Gao, Yitian
22 Lü, Xing
20 Tian, Shoufu
19 Khalique, Chaudry Masood
19 Zhang, Yi
18 Wang, Pan
16 Grammaticos, Basil
16 Ramani, Alfred
15 Dai, Zhengde
15 Jiang, Yan
15 Zayed, Elsayed M. E.
15 Zhang, Hongqing
14 Meng, Xianghua
13 Yu, Guofu
12 Nakamura, Yoshimasa
12 Ohta, Yasuhiro
11 Kudryashov, Nikolaĭ Alekseevich
11 Li, Min
11 Satsuma, Junkichi
11 Sun, Kun
11 Vitanov, Nikolay K.
11 Xu, Tao
11 Yu, Xin
11 Zhang, Haiqiang
10 Fan, Engui
10 Li, Jibin
10 Suris, Yuri Borisovich
10 Wang, Ming
10 Wen, Xiaoyong
10 Yan, Zhenya
10 Zhang, Tiantian
10 Zhang, Yingnan
9 Adem, Abdullahi Rashid
9 Biswas, Anjan
9 Geng, Xianguo
9 Guo, Boling
9 Iwasaki, Masashi
9 Petrera, Matteo
9 Qu, Qixing
9 Sun, Zhiyuan
9 Zhao, Junxiao
8 Ali Akbar, M.
8 Chang, Xiangke
8 Chen, Dengyuan
8 Dimitrova, Zlatinka I.
8 Feng, Baofeng
8 He, Jingsong
8 Li, Biao
8 Li, Chunxia
8 Lou, Senyue
8 Ma, Zhengyi
8 Nijhoff, Frank W.
8 Wang, Yufeng
8 Willox, Ralph
8 Xia, Tie-Cheng
8 Zhang, Yufeng
8 Zhao, Songlin
7 Ablowitz, Mark Jay
7 Alurrfi, Khaled A. E.
7 Chen, Junchao
7 Deng, Shufang
7 Dong, Huanhe
7 He, Yi
7 Kajiwara, Kenji
7 Kofané, Timoléon Crépin
7 Li, Shihao
7 Maruno, Kenichi
7 Shen, Shoufeng
7 Sun, Yepeng
7 Wang, Chuanjian
7 Wang, Dengshan
7 Zhang, Cheng
7 Zhao, Haiqiong
7 Zhu, Zuonong
6 Abassy, Tamer A.
6 Bratsos, Athanassios G.
6 Chen, Yong
6 Clarkson, Peter A.
6 Doliwa, Adam
6 Gubbiotti, Giorgio
6 Hirota, Ryogo
6 Hone, Andrew N. W.
6 Inoue, Rei
6 Jaradat, Husein M. M.
6 Liu, Hanze
6 Matveev, Vladimir B.
6 Mirzazadeh, Mohammad
6 Parker, Allen
6 Pogrebkov, Andrei K.
6 Quispel, Gilles Reinout Willem
6 Sahadevan, Ramajayam
6 Shan, Wenrui
6 Soliman, Ahmed Abo-Elmagd
...and 1,636 more Authors
all top 5

Cited in 236 Serials

173 Applied Mathematics and Computation
142 Journal of Mathematical Physics
108 Nonlinear Dynamics
61 Chaos, Solitons and Fractals
61 Communications in Nonlinear Science and Numerical Simulation
42 Computers & Mathematics with Applications
38 International Journal of Modern Physics B
37 Theoretical and Mathematical Physics
35 Applied Mathematics Letters
34 Journal of Nonlinear Mathematical Physics
30 Studies in Applied Mathematics
26 Mathematical Methods in the Applied Sciences
25 Physica D
25 Advances in Difference Equations
24 Abstract and Applied Analysis
22 Journal of Physics A: Mathematical and Theoretical
21 Communications in Mathematical Physics
20 Journal of Mathematical Analysis and Applications
20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
18 Mathematical Problems in Engineering
17 Physics Letters. A
17 Journal of Geometry and Physics
16 Letters in Mathematical Physics
16 Advances in Mathematical Physics
14 Wave Motion
14 Acta Applicandae Mathematicae
14 Communications in Theoretical Physics
12 Chaos
11 Journal of Shanghai University
11 Journal of Applied Analysis and Computation
10 International Journal of Theoretical Physics
10 Reports on Mathematical Physics
10 Journal of Computational and Applied Mathematics
10 Numerical Algorithms
10 International Journal of Computer Mathematics
10 Journal of the Egyptian Mathematical Society
10 Journal of Modern Optics
9 Complexity
9 Journal of Applied Mathematics
9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
8 Frontiers of Mathematics in China
8 East Asian Journal on Applied Mathematics
7 Modern Physics Letters B
7 Acta Mathematicae Applicatae Sinica. English Series
7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
7 International Journal of Applied and Computational Mathematics
6 Computers and Fluids
6 Japan Journal of Industrial and Applied Mathematics
6 Mathematical Physics, Analysis and Geometry
6 International Journal of Modern Physics C
6 Science China. Mathematics
6 Analysis and Mathematical Physics
5 Applicable Analysis
5 Computer Physics Communications
5 Journal of Fluid Mechanics
5 Nonlinearity
5 Nuclear Physics. B
5 Mathematics and Computers in Simulation
5 Mathematical and Computer Modelling
5 Computational Mathematics and Mathematical Physics
5 Linear Algebra and its Applications
5 Journal of Difference Equations and Applications
5 Journal of High Energy Physics
5 Journal of Applied Mathematics and Computing
5 Waves in Random and Complex Media
5 Discrete and Continuous Dynamical Systems. Series S
5 Symmetry
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik
4 Journal of Theoretical and Applied Mechanics (Sofia)
4 Advances in Mathematics
4 Aplikace Matematiky
4 Inventiones Mathematicae
4 Proceedings of the Japan Academy. Series A
4 Transactions of the American Mathematical Society
4 Applied Mathematics and Mechanics. (English Edition)
4 Acta Mechanica Sinica. (English Edition)
4 Applied Mathematics. Series B (English Edition)
4 Journal of Mathematical Sciences (New York)
4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
4 Regular and Chaotic Dynamics
4 International Journal of Nonlinear Sciences and Numerical Simulation
4 Nonlinear Analysis. Real World Applications
4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3 Modern Physics Letters A
3 Astrophysics and Space Science
3 Computer Methods in Applied Mechanics and Engineering
3 Journal of Computational Physics
3 Journal of the Franklin Institute
3 Physica A
3 Journal of Soviet Mathematics
3 Proceedings of the American Mathematical Society
3 Publications of the Research Institute for Mathematical Sciences, Kyoto University
3 Ricerche di Matematica
3 Numerical Methods for Partial Differential Equations
3 Journal of Nonlinear Science
3 International Journal of Numerical Methods for Heat & Fluid Flow
3 Journal of Mathematical Chemistry
3 The ANZIAM Journal
3 Journal of Systems Science and Complexity
3 Mathematical Modelling of Natural Phenomena
...and 136 more Serials
all top 5

Cited in 51 Fields

1,299 Partial differential equations (35-XX)
752 Dynamical systems and ergodic theory (37-XX)
159 Fluid mechanics (76-XX)
149 Numerical analysis (65-XX)
119 Difference and functional equations (39-XX)
77 Quantum theory (81-XX)
75 Ordinary differential equations (34-XX)
63 Computer science (68-XX)
56 Optics, electromagnetic theory (78-XX)
53 Statistical mechanics, structure of matter (82-XX)
45 Algebraic geometry (14-XX)
37 Special functions (33-XX)
33 Mechanics of particles and systems (70-XX)
31 Nonassociative rings and algebras (17-XX)
29 Differential geometry (53-XX)
28 Global analysis, analysis on manifolds (58-XX)
16 Mechanics of deformable solids (74-XX)
16 Biology and other natural sciences (92-XX)
15 Operator theory (47-XX)
14 Harmonic analysis on Euclidean spaces (42-XX)
13 Linear and multilinear algebra; matrix theory (15-XX)
11 Associative rings and algebras (16-XX)
9 Approximations and expansions (41-XX)
8 Combinatorics (05-XX)
8 Number theory (11-XX)
8 Integral equations (45-XX)
7 Topological groups, Lie groups (22-XX)
7 Relativity and gravitational theory (83-XX)
6 Commutative algebra (13-XX)
6 Probability theory and stochastic processes (60-XX)
6 Systems theory; control (93-XX)
5 Geophysics (86-XX)
4 History and biography (01-XX)
4 Convex and discrete geometry (52-XX)
4 Astronomy and astrophysics (85-XX)
4 Information and communication theory, circuits (94-XX)
3 Group theory and generalizations (20-XX)
3 Real functions (26-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Geometry (51-XX)
2 Measure and integration (28-XX)
2 Functions of a complex variable (30-XX)
2 Integral transforms, operational calculus (44-XX)
2 Functional analysis (46-XX)
2 Statistics (62-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 General and overarching topics; collections (00-XX)
1 Mathematical logic and foundations (03-XX)
1 Field theory and polynomials (12-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Manifolds and cell complexes (57-XX)

Citations by Year

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