×
Compute Distance To:
Author ID: hirota.ryogo Recent zbMATH articles by "Hirota, Ryogo"
Published as: Hirota, Ryogo; Hirota, R.; Hirota, Ryōgo
External Links: Wikidata · GND · IdRef
Documents Indexed: 61 Publications since 1960, including 1 Book
1 Further Contribution
Co-Authors: 18 Co-Authors with 32 Joint Publications
373 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

48 Publications have been cited 2,409 times in 1,869 Documents Cited by Year
Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons. Zbl 1168.35423
Hirota, Ryogo
746
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
297
2004
Exact envelope-soliton solutions of a nonlinear wave equation. Zbl 0257.35052
Hirota, Ryogo
261
1973
A new form of Bäcklund transformations and its relation to the inverse scattering problem. Zbl 1168.37322
Hirota, Ryogo
133
1974
Exact N-soliton solutions of the wave equations of long waves in shallow- water and in nonlinear lattices. Zbl 0261.76008
Hirota, Ryogo
121
1973
\(N\)-soliton solutions of model equations for shallow water waves. Zbl 1334.76016
Hirota, Ryogo; Satsuma, Junkichi
108
1976
Nonlinear partial difference equations. I: A difference analogue of the Korteweg-de Vries equation. Zbl 1334.39013
Hirota, Ryogo
69
1977
Hierarchies of coupled soliton equations. I. Zbl 1160.37395
Hirota, Ryogo; Ohta, Yasuhiro
64
1991
Theory of solid state plasma waveguide in a transverse magnetic field. Zbl 0124.21603
Hirota, R.
56
1964
Nonlinear partial difference equations. II: Discrete-time Toda equation. Zbl 1334.39014
Hirota, Ryogo
54
1977
Nonlinear partial difference equations. III: Discrete sine-Gordon equation. Zbl 1334.39015
Hirota, Ryogo
54
1977
Nonlinear evolution equations generated from the Bäcklund transformation for the Boussinesq equation. Zbl 1098.81547
Hirota, Ryogo; Satsuma, Junkichi
41
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
32
2003
Direct method of finding exact solutions of nonlinear evolution equations. Zbl 0336.35024
Hirota, Ryogo
29
1976
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
Soliton solutions of a coupled modified KdV equations. Zbl 0946.35078
Iwao, Masataka; Hirota, Ryogo
26
1997
Discretization of the Euler top. Zbl 1058.70504
Hirota, Ryogo; Kimura, Kinji
25
2000
Conserved quantities of a class of nonlinear difference-difference equations. Zbl 0972.39501
Hirota, Ryogo; Tsujimoto, Satoshi
24
1995
How to find the conserved quantities of nonlinear discrete equations. Zbl 0998.39010
Hirota, Ryogo; Kimura, Kinji; Yahagi, Hideyuki
24
2001
Soliton structure of the Drinfel’d-Sokolov-Wilson equation. Zbl 0638.35071
Hirota, R.; Grammaticos, B.; Ramani, A.
21
1986
Discretization of the Lagrange top. Zbl 1058.70506
Kimura, Kinji; Hirota, Ryogo
20
2000
Pfaffian representation of solutions to the discrete BKP hierarchy in bilinear form. Zbl 0948.39007
Tsujimoto, Satoshi; Hirota, Ryogo
18
1996
Difference scheme of soliton equations. Zbl 0900.35332
Hirota, Ryogo; Tsujimoto, Satoshi; Imai, Tatsuya
15
1993
Nonlinear evolution equations generated from the Bäcklund transformation for the Toda lattice. Zbl 1079.35536
Hirota, Ryogo; Satsuma, Junkichi
14
1976
A new class of integrable discrete systems. Zbl 1042.37012
Kimura, K.; Yahagi, H.; Hirota, R.; Ramani, A.; Grammaticos, B.; Ohta, Y.
14
2002
Time-discretization of soliton equations. Zbl 0961.35135
Hirota, Ryogo; Iwao, Masataka
11
2000
Ultradiscrete KdV equation. Zbl 0948.39008
Tsujimoto, Satoshi; Hirota, Ryogo
10
1998
Conserved quantities of “random-time Toda equation”. Zbl 0942.82014
Hirota, Ryogo
10
1997
Nonlinear partial difference equations. IV: Bäcklund transformations for the discrete-time Toda equation. Zbl 1334.39016
Hirota, Ryogo
10
1978
Second modified KdV equation and its exact multisoliton solution. Zbl 1334.35292
Nakamura, Akira; Hirota, Ryogo
9
1980
“Molecule solutions” of coupled modified KdV equations. Zbl 0944.35074
Hirota, Ryogo
8
1997
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
8
1996
The Bäcklund and inverse scattering transform of the K-dV equation with nonuniformities. Zbl 1334.81103
Hirota, Ryogo
8
1979
Soliton equations exhibiting Pfaffian solutions. Zbl 0986.35093
Hirota, Ryogo; Iwao, Masataka; Tsujimoto, Satoshi
6
2001
Reduction of soliton equations in bilinear form. Zbl 0601.35099
Hirota, Ryogo
6
1986
Discretization of coupled modified KdV equations. Zbl 1115.37345
Hirota, Ryogo
5
2000
Discretization of coupled soliton equations. Zbl 1131.35382
Hirota, Ryogo
3
2006
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
New solutions to the ultradiscrete soliton equations. Zbl 1173.39005
Hirota, Ryogo
3
2009
The Bäcklund transformation equations for the ultradiscrete KP equation. Zbl 1052.37056
Shinzawa, Nobuhiko; Hirota, Ryogo
3
2003
Discretization of the new type of soliton equations. Zbl 1223.35276
Hirota, Ryogo; Ohta, Yasuhiro
3
2007
“Recurrence equations”, an integrable system. Zbl 1065.39034
Hirota, Ryogo; Yahagi, Hideyuki
1
2002
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
Bilinear forms of soliton equations. Zbl 0539.70027
Hirota, Ryogo
1
1983
Ultradiscretization of the Tzitzeica equation. Zbl 1076.37065
Hirota, Ryogo; Takahashi, Daisuke
1
2005
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
Addition formula for Pfaffians. Zbl 1301.39003
Hirota, Ryogo
1
2013
New solutions to the ultradiscrete soliton equations. Zbl 1173.39005
Hirota, Ryogo
3
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
3
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
297
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
32
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.
14
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
24
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
25
2000
Discretization of the Lagrange top. Zbl 1058.70506
Kimura, Kinji; Hirota, Ryogo
20
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
5
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
10
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
26
1997
Conserved quantities of “random-time Toda equation”. Zbl 0942.82014
Hirota, Ryogo
10
1997
“Molecule solutions” of coupled modified KdV equations. Zbl 0944.35074
Hirota, Ryogo
8
1997
Pfaffian representation of solutions to the discrete BKP hierarchy in bilinear form. Zbl 0948.39007
Tsujimoto, Satoshi; Hirota, Ryogo
18
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
8
1996
Conserved quantities of a class of nonlinear difference-difference equations. Zbl 0972.39501
Hirota, Ryogo; Tsujimoto, Satoshi
24
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
15
1993
Hierarchies of coupled soliton equations. I. Zbl 1160.37395
Hirota, Ryogo; Ohta, Yasuhiro
64
1991
Soliton structure of the Drinfel’d-Sokolov-Wilson equation. Zbl 0638.35071
Hirota, R.; Grammaticos, B.; Ramani, A.
21
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
10
1978
Nonlinear partial difference equations. I: A difference analogue of the Korteweg-de Vries equation. Zbl 1334.39013
Hirota, Ryogo
69
1977
Nonlinear partial difference equations. II: Discrete-time Toda equation. Zbl 1334.39014
Hirota, Ryogo
54
1977
Nonlinear partial difference equations. III: Discrete sine-Gordon equation. Zbl 1334.39015
Hirota, Ryogo
54
1977
Nonlinear evolution equations generated from the Bäcklund transformation for the Boussinesq equation. Zbl 1098.81547
Hirota, Ryogo; Satsuma, Junkichi
41
1977
\(N\)-soliton solutions of model equations for shallow water waves. Zbl 1334.76016
Hirota, Ryogo; Satsuma, Junkichi
108
1976
Direct method of finding exact solutions of nonlinear evolution equations. Zbl 0336.35024
Hirota, Ryogo
29
1976
Nonlinear evolution equations generated from the Bäcklund transformation for the Toda lattice. Zbl 1079.35536
Hirota, Ryogo; Satsuma, Junkichi
14
1976
A new form of Bäcklund transformations and its relation to the inverse scattering problem. Zbl 1168.37322
Hirota, Ryogo
133
1974
Exact envelope-soliton solutions of a nonlinear wave equation. Zbl 0257.35052
Hirota, Ryogo
261
1973
Exact N-soliton solutions of the wave equations of long waves in shallow- water and in nonlinear lattices. Zbl 0261.76008
Hirota, Ryogo
121
1973
Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons. Zbl 1168.35423
Hirota, Ryogo
746
1971
Theory of solid state plasma waveguide in a transverse magnetic field. Zbl 0124.21603
Hirota, R.
56
1964
all top 5

Cited by 2,027 Authors

86 Wazwaz, Abdul-Majid Abdul-Rahman
64 Tian, Bo
45 Ma, Wen-Xiu
36 Hu, Xingbiao
30 Liu, Wenjun J.
30 Zhang, Dajun
29 Zhang, Sheng
25 Lü, Xing
25 Tian, Shoufu
24 Gao, Yitian
22 Khalique, Chaudry Masood
20 Zhang, Yi
19 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
14 Yan, Zhenya
13 Nakamura, Yoshimasa
13 Ohta, Yasuhiro
13 Yu, Guofu
12 Qu, Qixing
12 Zhang, Yingnan
11 Fan, Engui
11 Guo, Boling
11 He, Jingsong
11 Kudryashov, Nikolaĭ Alekseevich
11 Li, Min
11 Satsuma, Junkichi
11 Sun, Kun
11 Suris, Yuri Borisovich
11 Vitanov, Nikolay K.
11 Wen, Xiaoyong
11 Xu, Tao
11 Yu, Xin
11 Zhang, Haiqiang
11 Zhang, Tiantian
11 Zhang, Yufeng
10 Adem, Abdullahi Rashid
10 Biswas, Anjan
10 Chang, Xiangke
10 Chen, Yong
10 Feng, Baofeng
10 Geng, Xianguo
10 He, Yi
10 Iwasaki, Masashi
10 Kofané, Timoléon Crépin
10 Li, Jibin
10 Wang, Ming
9 Ali Akbar, M.
9 Lou, Senyue
9 Petrera, Matteo
9 Sun, Zhiyuan
9 Zhao, Junxiao
9 Zhu, Zuonong
8 Chen, Dengyuan
8 Deng, Shufang
8 Dimitrova, Zlatinka I.
8 Doliwa, Adam
8 Li, Biao
8 Li, Chunxia
8 Ma, Zhengyi
8 Matveev, Vladimir B.
8 Nijhoff, Frank W.
8 Seadawy, Aly R.
8 Wang, Yufeng
8 Willox, Ralph
8 Xia, Tie-Cheng
8 Xu, Bo
8 Zhao, Haiqiong
8 Zhao, Songlin
7 Ablowitz, Mark Jay
7 Alurrfi, Khaled A. E.
7 Chen, Junchao
7 Dong, Huanhe
7 Gegenhasi
7 Gubbiotti, Giorgio
7 Inc, Mustafa
7 Kajiwara, Kenji
7 Li, Bangqing
7 Li, Shihao
7 Lin, Ji
7 Ling, Liming
7 Maruno, Kenichi
7 Quispel, Gilles Reinout Willem
7 Shan, Wenrui
7 Shen, Shoufeng
7 Sun, Jianqing
7 Sun, Yepeng
7 Tokihiro, Tetsuji
7 Triki, Houria
7 Wang, Chuanjian
7 Wang, Dengshan
7 Yaşar, Emrullah
7 Zhang, Cheng
7 Zhen, Hui-Ling
7 Zhou, Qin
...and 1,927 more Authors
all top 5

Cited in 260 Serials

177 Applied Mathematics and Computation
146 Journal of Mathematical Physics
108 Nonlinear Dynamics
75 Chaos, Solitons and Fractals
66 Communications in Nonlinear Science and Numerical Simulation
43 Theoretical and Mathematical Physics
43 Applied Mathematics Letters
42 Computers & Mathematics with Applications
39 International Journal of Modern Physics B
35 Journal of Nonlinear Mathematical Physics
34 Physica D
31 Advances in Difference Equations
30 Studies in Applied Mathematics
26 Mathematical Methods in the Applied Sciences
24 Physics Letters. A
24 Abstract and Applied Analysis
22 Communications in Mathematical Physics
22 Journal of Geometry and Physics
22 Journal of Physics A: Mathematical and Theoretical
21 Journal of Mathematical Analysis and Applications
21 Advances in Mathematical Physics
20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
19 Letters in Mathematical Physics
19 Wave Motion
18 Mathematical Problems in Engineering
15 Acta Applicandae Mathematicae
15 Communications in Theoretical Physics
14 Numerical Algorithms
14 International Journal of Computer Mathematics
14 Waves in Random and Complex Media
13 International Journal of Applied and Computational Mathematics
12 Chaos
12 Journal of Applied Analysis and Computation
11 Reports on Mathematical Physics
11 Journal of Shanghai University
11 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
10 International Journal of Theoretical Physics
10 Journal of Computational and Applied Mathematics
10 Journal of the Egyptian Mathematical Society
10 Mathematical Physics, Analysis and Geometry
10 Journal of Modern Optics
10 AIMS Mathematics
9 Mathematics and Computers in Simulation
9 Complexity
9 Journal of Applied Mathematics
9 East Asian Journal on Applied Mathematics
8 Nuclear Physics. B
8 Acta Mathematicae Applicatae Sinica. English Series
8 Frontiers of Mathematics in China
7 Modern Physics Letters B
7 Japan Journal of Industrial and Applied Mathematics
7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
7 Qualitative Theory of Dynamical Systems
7 Analysis and Mathematical Physics
6 Computers and Fluids
6 Journal of Difference Equations and Applications
6 International Journal of Modern Physics C
6 Discrete and Continuous Dynamical Systems. Series S
6 Science China. Mathematics
6 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
5 Applicable Analysis
5 Computer Physics Communications
5 Journal of Fluid Mechanics
5 Nonlinearity
5 Mathematical and Computer Modelling
5 Computational Mathematics and Mathematical Physics
5 Linear Algebra and its Applications
5 Applied Mathematics. Series B (English Edition)
5 Journal of High Energy Physics
5 International Journal of Nonlinear Sciences and Numerical Simulation
5 Journal of Applied Mathematics and Computing
5 Symmetry
5 Journal of Applied Nonlinear Dynamics
4 Journal of Computational Physics
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 American Mathematical Society
4 Proceedings of the Japan Academy. Series A
4 Publications of the Research Institute for Mathematical Sciences, Kyoto University
4 Transactions of the American Mathematical Society
4 Applied Mathematics and Mechanics. (English Edition)
4 Acta Mechanica Sinica. (English Edition)
4 Journal of Nonlinear Science
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 Nonlinear Analysis. Real World Applications
4 Mathematical Modelling of Natural Phenomena
4 Advances in Applied Mathematics and Mechanics
4 Journal of Computational Dynamics
4 Journal of Function Spaces
3 Modern Physics Letters A
3 Astrophysics and Space Science
3 Computer Methods in Applied Mechanics and Engineering
3 Journal of the Franklin Institute
3 Physica A
3 Journal of Differential Equations
...and 160 more Serials
all top 5

Cited in 52 Fields

1,463 Partial differential equations (35-XX)
838 Dynamical systems and ergodic theory (37-XX)
177 Fluid mechanics (76-XX)
162 Numerical analysis (65-XX)
135 Difference and functional equations (39-XX)
89 Quantum theory (81-XX)
80 Ordinary differential equations (34-XX)
73 Computer science (68-XX)
71 Optics, electromagnetic theory (78-XX)
65 Statistical mechanics, structure of matter (82-XX)
51 Algebraic geometry (14-XX)
38 Special functions (33-XX)
34 Mechanics of particles and systems (70-XX)
32 Nonassociative rings and algebras (17-XX)
32 Differential geometry (53-XX)
30 Global analysis, analysis on manifolds (58-XX)
26 Mechanics of deformable solids (74-XX)
18 Operator theory (47-XX)
18 Biology and other natural sciences (92-XX)
15 Harmonic analysis on Euclidean spaces (42-XX)
14 Linear and multilinear algebra; matrix theory (15-XX)
14 Approximations and expansions (41-XX)
11 Associative rings and algebras (16-XX)
10 Real functions (26-XX)
9 Combinatorics (05-XX)
9 Integral equations (45-XX)
9 Relativity and gravitational theory (83-XX)
8 Number theory (11-XX)
8 Topological groups, Lie groups (22-XX)
8 Probability theory and stochastic processes (60-XX)
6 Commutative algebra (13-XX)
6 Geophysics (86-XX)
6 Systems theory; control (93-XX)
5 Astronomy and astrophysics (85-XX)
4 History and biography (01-XX)
4 Functions of a complex variable (30-XX)
4 Several complex variables and analytic spaces (32-XX)
4 Geometry (51-XX)
4 Convex and discrete geometry (52-XX)
4 Information and communication theory, circuits (94-XX)
3 Group theory and generalizations (20-XX)
3 Functional analysis (46-XX)
3 Statistics (62-XX)
2 Measure and integration (28-XX)
2 Integral transforms, operational calculus (44-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 \(K\)-theory (19-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Manifolds and cell complexes (57-XX)

Citations by Year

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.