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Grammaticos, Basil

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Author ID: grammaticos.basil Recent zbMATH articles by "Grammaticos, Basil"
Published as: Grammaticos, B.; Grammaticos, Basile; Grammaticos, Basil
Homepage: http://www.imnc.univ-paris7.fr/basile/
External Links: Math-Net.Ru
Documents Indexed: 265 Publications since 1982, including 3 Books

Publications by Year

Citations contained in zbMATH Open

204 Publications have been cited 1,779 times in 915 Documents Cited by Year
Do integrable mappings have the Painlevé property? Zbl 0990.37518
Grammaticos, B.; Ramani, A.; Papageorgiou, V.
124
1991
Discrete versions of the Painlevé equations. Zbl 1050.39500
Ramani, A.; Grammaticos, B.; Hietarinta, J.
110
1991
Structural stability of the Korteweg-de Vries solitons under a singular perturbation. Zbl 0695.35161
Pomeau, Y.; Ramani, A.; Grammaticos, B.
65
1988
Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable? Zbl 0619.35086
Dorizzi, B.; Grammaticos, B.; Ramani, A.; Winternitz, P.
57
1986
From continuous to discrete Painlevé equations. Zbl 0794.34013
Fokas, A. S.; Grammaticos, B.; Ramani, A.
43
1993
Integrability of Hamiltonians with third- and fourth-degree polynomial potentials. Zbl 0547.70017
Grammaticos, B.; Dorizzi, B.; Ramani, Alfred
35
1983
Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system. Zbl 0714.34005
Grammaticos, B.; Moulin-Ollagnier, Jean; Ramani, A.; Strelcyn, Jean-Marie; Wojciechowski, S.
33
1990
A new class of integrable systems. Zbl 0547.70016
Dorizzi, B.; Grammaticos, B.
33
1983
Integrable Hamiltonian systems with velocity-dependent potentials. Zbl 0586.70013
Dorizzi, B.; Grammaticos, B.; Ramani, A.; Winternitz, P.
31
1985
Discrete Painlevé equations: coalescences, limits and degeneracies. Zbl 0912.34011
Ramani, A.; Grammaticos, B.
30
1996
Discrete Painlevé equations. Zbl 1014.39013
Grammaticos, Basile; Nijhoff, Frank W.; Ramani, Alfred
28
1999
On the complete and partial integrability of non-Hamiltonian systems. Zbl 0599.34002
Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.
24
1984
Discrete Painlevé equations: a review. Zbl 1064.39019
Grammaticos, B.; Ramani, A.
22
2004
Lie symmetries of a generalised nonlinear Schrödinger equation. III: Reductions to third-order ordinary differential equations. Zbl 0707.35146
Gagnon, L.; Grammaticos, B.; Ramani, A.; Winternitz, P.
22
1989
Integrable lattices and convergence acceleration algorithms. Zbl 0910.65001
Papageorgiou, V.; Grammaticos, B.; Ramani, A.
22
1993
Soliton structure of the Drinfel’d-Sokolov-Wilson equation. Zbl 0638.35071
Hirota, R.; Grammaticos, B.; Ramani, A.
20
1986
On the autonomous limit of discrete Painlevé equations. Zbl 0992.39015
Ramani, A.; Carstea, A. S.; Grammaticos, B.; Ohta, Y.
19
2002
On discrete Painlevé equations associated with the lattice KdV systems and the Painlevé VI equation. Zbl 1152.39313
Nijhoff, F. W.; Ramani, A.; Grammaticos, B.; Ohta, Y.
19
2001
Hamiltonians with high-order integrals and the ”weak-Painlevé” concept. Zbl 0549.70009
Grammaticos, B.; Dorizzi, B.; Ramani, A.
19
1984
On a novel \(q\)-discrete analogue of the Painlevé VI equation. Zbl 0938.39020
Grammaticos, B.; Ramani, A.
18
1999
An affine Weyl group approach to the eight-parameter discrete Painlevé equation. Zbl 1002.39029
Ohta, Y.; Ramani, A.; Grammaticos, B.
18
2001
Epidemic dynamics: discrete-time and cellular automaton models. Zbl 1026.92042
Willox, R.; Grammaticos, B.; Carstea, A. S.; Ramani, A.
17
2003
The Gambier mapping, revisited. Zbl 0910.58017
Grammaticos, B.; Ramani, A.; Lafortune, S.
17
1998
Asymmetric discrete Painlevé equations. Zbl 0983.34083
Kruskal, M. D.; Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.
16
2000
Integrable lattice equations and their growth properties. Zbl 1072.37509
Tremblay, S.; Grammaticos, B.; Ramani, A.
16
2001
Orthogonal polynomial approach to discrete Lax pairs for initial boundary-value problems of the QD algorithm. Zbl 0831.58028
Papageorgiou, V.; Grammaticos, B.; Ramani, A.
16
1995
Special function solutions of the discrete Painlevé equations. Zbl 0994.33500
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M.
15
2001
How to detect the integrability of discrete systems. Zbl 1183.37001
Grammaticos, B.; Halburd, R. G.; Ramani, A.; Viallet, C-M
15
2009
Constructing the soliton solutions for the \(N=1\) supersymmetric KdV hierarchy. Zbl 1067.37107
Carstea, A. S.; Ramani, A.; Grammaticos, B.
14
2001
A study of the alternate discrete Painlevé II equation. Zbl 0860.35124
Nijhoff, F.; Satsuma, J.; Kajiwara, K.; Grammaticos, B.; Ramani, A.
13
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
Miura transforms for discrete Painlevé equations. Zbl 0754.35149
Ramani, A.; Grammaticos, B.
13
1992
Degeneration through coalescence of the \(q\)-Painlevé VI equation. Zbl 0932.39017
Grammaticos, B.; Ohta, Y.; Ramani, A.; Sakai, H.
12
1998
Solvable chaos. Zbl 1369.37046
Grammaticos, B.; Ramani, A.; Viallet, C. M.
12
2005
On the integrability of correspondences associated to integral curves. Zbl 1118.81454
Viallet, C. M.; Grammaticos, B.; Ramani, A.
12
2004
A class of integrable and nonintegrable mappings and their dynamics. Zbl 1129.37032
Tsuda, Teruhisa; Grammaticos, Basil; Ramani, Alfred; Takenawa, Tomoyuki
12
2007
Discrete integrable systems. Proceedings of the international CIMPA school, Pondicherry, India, February 2–14, 2003. Zbl 1052.37002
Grammaticos, B. (ed.); Kosmann-Schwarzbach, Y. (ed.); Tamizhmani, T. (ed.)
11
2004
Linearizable QRT mappings. Zbl 1246.37090
Ramani, A.; Grammaticos, B.; Satsuma, J.; Mimura, N.
11
2011
Integrable systems without the Painlevé property. Zbl 0953.34077
Ramani, A.; Grammaticos, B.; Tremblay, S.
11
2000
Quadratic relations in continuous and discrete Painlevé equations. Zbl 0953.34078
Ramani, A.; Grammaticos, B.; Tamizhmani, T.
11
2000
Discrete integrable systems from continuous Painlevé equations through limiting procedures. Zbl 0963.37069
Ramani, A.; Ohta, Y.; Grammaticos, B.
11
2000
The weak-Painlevé property as a criterion for the integrability of dynamical systems. Zbl 0613.34036
Rañada, A. F.; Ramani, A.; Dorizzi, B.; Grammaticos, B.
11
1985
Deconstructing an integrable lattice equation. Zbl 1086.37037
Ramani, A.; Joshi, N.; Grammaticos, B.; Tamizhmani, T.
11
2006
Generalized separability for a Hamiltonian with nonseparable quartic potential. Zbl 0961.70502
Ravoson, V.; Ramani, A.; Grammaticos, B.
10
1994
A bilinear approach to discrete Miura transformations. Zbl 1044.37547
Joshi, N.; Ramani, A.; Grammaticos, B.
10
1998
Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations. Zbl 0939.37041
Ohta, Y.; Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.
10
1999
On a transcendental equation related to Painlevé III, and its discrete forms. Zbl 0948.34070
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M.
10
2000
Bilinearization and soliton solutions of the \(N=1\) supersymmetric sine-Gordon equation. Zbl 0980.35147
Grammaticos, B.; Ramani, A.; Carstea, A. S.
10
2001
Growth and integrability in discrete systems. Zbl 1006.39018
Grammaticos, B.; Tamizhmani, T.; Ramani, A.; Tamizhmani, K. M.
10
2001
Bilinear structure and Schlesinger transforms of the \(q\)-P\(_{III}\) and \(q\)-P\(_{VI}\) equations. Zbl 0911.34007
Jimbo, M.; Sakai, H.; Ramani, A.; Grammaticos, B.
10
1996
Singularity analysis for difference Painlevé equations associated with the affine Weyl group \(E_8\). Zbl 1359.39005
Ramani, A.; Grammaticos, B.
10
2017
Discrete Painlevé equations: Derivation and properties. Zbl 0793.35093
Grammaticos, B.; Ramani, A.
10
1993
From continuous Painlevé IV to the asymmetric discrete Painlevé. I. Zbl 0910.34019
Grammaticos, B.; Ramani, A.
10
1998
Self-duality and Schlesinger chains for the asymmetric \(\text{d-P}_{\text{II}}\) and \(\text{q-P}_{\text{III}}\) equations. Zbl 0911.39007
Ramani, A.; Ohta, Y.; Satsuma, J.; Grammaticos, B.
10
1998
Painlevé analysis for the mixmaster universe model. Zbl 0811.53086
Contopoulos, G.; Grammaticos, B.; Ramani, A.
10
1993
From integrable lattices to non-QRT mappings. Zbl 1111.39013
Joshi, N.; Grammaticos, B.; Tamizhmani, T.; Ramani, A.
10
2006
Elliptic and multiplicative discrete Painlevé equations from the affine Weyl group \(E_{8}\). Zbl 1315.39002
Grammaticos, B.; Ramani, A.
10
2015
On the non-integrability of some generalized Toda lattices. Zbl 0667.58021
Yoshida, H.; Ramani, A.; Grammaticos, B.; Hietarinta, J.
10
1987
Linearization and solutions of the discrete Painlevé III equation. Zbl 0941.34502
Grammaticos, B.; Nijhoff, F. W.; Papageorgiou, V.; Ramani, A.; Satsuma, J.
9
1994
Bilinear discrete Painlevé equations. Zbl 0867.39001
Ramani, A.; Grammaticos, B.; Satsuma, J.
9
1995
A search for integrable bilinear equations: The Painlevé approach. Zbl 0729.35133
Grammaticos, B.; Ramani, A.; Hietarinta, J.
9
1990
Deautonomization by singularity confinement: an algebro-geometric justification. Zbl 1371.39011
Mase, T.; Willox, R.; Grammaticos, B.; Ramani, A.
9
2015
Linearizable mappings and the low-growth criterion. Zbl 0962.37020
Ramani, A.; Grammaticos, B.; Lafortune, S.; Ohta, Y.
9
2000
The mixmaster universe model, revisited. Zbl 0844.58120
Contopoulos, G.; Grammaticos, B.; Ramani, A.
9
1994
Bilinearization and solutions of the KdV6 equation. Zbl 1155.35440
Ramani, A.; Grammaticos, B.; Willox, R.
9
2008
A bilinear approach to the discrete Painlevé I equations. Zbl 1074.39023
Grammaticos, B.; Tamizhmani, T.; Ramani, A.; Carstea, A. S.; Tamizhmani, K. M.
8
2002
The hunting for the discrete Painlevé equations. Zbl 0951.39005
Grammaticos, B.; Ramani, A.
8
2000
Casorati determinant solutions for the discrete Painlevé-II equation. Zbl 0811.35150
Kajiwara, Kenji; Ohta, Yasuhiro; Satsuma, Junkichi; Grammaticos, Basil; Ramani, Alfred
8
1994
Strongly asymmetric discrete Painlevé equations: the additive case. Zbl 1295.39003
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
8
2014
Delay-differential equations and the Painlevé transcendents. Zbl 0803.34008
Grammaticos, B.; Ramani, A.; Moreira, I. C.
8
1993
Non-integrability of the fourth-order truncated Toda Hamiltonian. Zbl 0656.58014
Yoshida, H.; Ramani, A.; Grammaticos, B.
8
1988
Explicit integrability for Hamiltonian systems and the Painlevé conjecture. Zbl 0566.70020
Dorizzi, B.; Grammaticos, B.; Ramani, A.
8
1984
On a novel representation of discrete Painlevé equations. Zbl 1323.39004
Grammaticos, B.; Ramani, A.
8
2015
Discrete Painlevé equations associated with the affine Weyl group \(E_{8}\). Zbl 1326.39006
Ramani, A.; Grammaticos, B.
8
2015
Constructing solutions to the ultradiscrete Painlevé equations. Zbl 0926.39007
Takahashi, D.; Tokihiro, T.; Grammaticos, B.; Ohta, Y.; Ramani, A.
7
1997
Bilinear discrete Painlevé-II and its particular solutions. Zbl 0859.34073
Satsuma, J.; Kajiwara, K.; Grammaticos, B.; Hietarinta, J.; Ramani, A.
7
1995
The space of initial conditions for linearizable mappings. Zbl 1021.37023
Takenawa, T.; Eguchi, M.; Grammaticos, B.; Ohta, Y.; Ramani, A.; Satsuma, J.
7
2003
The number of discrete Painlevé equations is infinite. Zbl 1233.34038
Ramani, A.; Grammaticos, B.
7
2009
Lie symmetries of Hirota’s bilinear equations. Zbl 0737.35110
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.
7
1991
Integrability – and how to detect it. Zbl 0904.58028
Grammaticos, B.; Ramani, A.
7
1997
The redemption of singularity confinement. Zbl 1312.37043
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Kanki, M.
7
2015
Painlevé resonances versus Kowalevski exponents: Some exact results on singularity structure and integrability of dynamical systems. Zbl 0631.70012
Yoshida, H.; Grammaticos, B.; Ramani, A.
7
1987
Ultradiscretization without positivity. Zbl 1095.93001
Isojima, S.; Grammaticos, B.; Ramani, A.; Satsuma, J.
7
2006
Singularity structure and algebraic properties of the differential-difference Kadomtsev-Petviashvili equation. Zbl 1121.37318
Tamizhmani, K. M.; Kanagavel, S.; Grammaticos, B.; Ramani, A.
6
2000
A unified description of the asymmetric \(q\text{-P}_{\text{V}}\) and \(d\text{-P}_{\text{IV}}\) equations and their Schlesinger transformations. Zbl 1034.34104
Grammaticos, B.; Ramani, A.; Ohta, Y.
6
2003
From the continuous P\(_{\text{V}}\) to discrete Painlevé equations. Zbl 1046.39013
Tokihiro, T.; Grammaticos, B.; Ramani, A.
6
2002
Elliptic discrete Painlevé equations. Zbl 1056.39027
Ohta, Y.; Ramani, A.; Grammaticos, B.
6
2002
The road to the discrete analogue of the Painlevé property: Nevanlinna meets singularity confinement. Zbl 1057.39018
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M.
6
2003
Painlevé analysis and singularity confinement: The ultimate conjecture. Zbl 0773.35076
Ramani, A.; Grammaticos, B.; Tamizhmani, K. M.
6
1993
Discretising the Painlevé equations à la Hirota-Mickens. Zbl 1274.34261
Grammaticos, B.; Ramani, A.; Satsuma, J.; Willox, R.
6
2012
Strongly asymmetric discrete Painlevé equations: the multiplicative case. Zbl 1383.39019
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
6
2016
Singularity confinement and full-deautonomisation: a discrete integrability criterion. Zbl 1364.39001
Grammaticos, B.; Ramani, A.; Willox, R.; Mase, T.; Satsuma, J.
6
2015
Schlesinger transforms for the discrete Painlevé IV equation. Zbl 0789.39001
Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.
6
1993
Linearization and solutions of the discrete Painlevé III equation. Zbl 0909.39004
Grammaticos, B.; Nijhoff, F. W.; Papageorgiou, V.; Ramani, A.; Satsuma, J.
6
1994
The Gambier mapping. Zbl 0909.39005
Grammaticos, B.; Ramani, A.
6
1996
Nonintegrability of \((2+1)\)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis. Zbl 1160.81394
Kumar, C. Senthil; Lakshmanan, M.; Grammaticos, B.; Ramani, A.
6
2006
Integrability and the Painlevé property for low-dimensional systems. Zbl 0553.34032
Ramani, A.; Dorizzi, B.; Grammaticos, B.; Bountis, T.
6
1984
From discrete to continuous Painlevé equations: a bilinear approach. Zbl 0972.35529
Ohta, Y.; Ramani, A.; Grammaticos, B.; Tamizhmani, K. M.
5
1996
Linearisable supersymmetric equations. Zbl 1004.34028
Carstea, A. S.; Ramani, A.; Grammaticos, B.
5
2002
The last remake of the mixmaster universe model. Zbl 0866.53066
Contopoulos, G.; Grammaticos, B.; Ramani, A.
5
1995
Constructing discrete Painlevé equations: from \(\mathrm{E}_8^{(1)}\) to \(\mathrm{A}_1^{(1)}\) and back. Zbl 1418.37113
Ramani, A.; Grammaticos, B.; Willox, R.; Tamizhmani, T.
1
2019
Restoring discrete Painlevé equations from an \(\mathrm{E}_8^{(1)}\)-associated one. Zbl 1416.39003
Grammaticos, B.; Ramani, A.; Willox, R.
1
2019
On the canonical forms of QRT mappings and discrete Painlevé equations. Zbl 1406.39007
Ramani, A.; Grammaticos, B.; Satsuma, J.; Tamizhmani, T.
3
2018
Integrable mappings and the notion of anticonfinement. Zbl 1405.37063
Mase, T.; Willox, R.; Ramani, A.; Grammaticos, B.
2
2018
Calculating the algebraic entropy of mappings with unconfined singularities. Zbl 1397.37062
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Satsuma, J.
1
2018
Investigating relations between discrete Painlevé equations: the multistep approach. Zbl 1403.39006
Ramani, A.; Grammaticos, B.; Tamizhmani, T.
1
2018
Singularity analysis for difference Painlevé equations associated with the affine Weyl group \(E_8\). Zbl 1359.39005
Ramani, A.; Grammaticos, B.
10
2017
A systematic method for constructing discrete Painlevé equations in the degeneration cascade of the \(\operatorname{E}_8\) group. Zbl 1391.37053
Willox, R.; Ramani, A.; Grammaticos, B.
4
2017
Calculating algebraic entropies: an express method. Zbl 1390.81106
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.
4
2017
On the limits of discrete Painlevé equations associated with the affine Weyl group \(E_{8}\). Zbl 1362.39017
Tamizhmani, K. M.; Tamizhmani, T.; Ramani, A.; Grammaticos, B.
4
2017
Miura transformations for discrete Painlevé equations coming from the affine \(\operatorname{E}_{8}\) Weyl group. Zbl 1365.39003
Ramani, A.; Grammaticos, B.; Willox, R.
3
2017
Strongly asymmetric discrete Painlevé equations: the multiplicative case. Zbl 1383.39019
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
6
2016
From trihomographic to elliptic Painlevé equations. Zbl 1354.39005
Grammaticos, B.; Ramani, A.
4
2016
Parameterless discrete Painlevé equations and their Miura relations. Zbl 1420.34105
Grammaticos, B.; Ramani, A.
3
2016
Full-deautonomisation of a lattice equation. Zbl 1353.37138
Willox, R.; Mase, T.; Ramani, A.; Grammaticos, B.
1
2016
Elliptic and multiplicative discrete Painlevé equations from the affine Weyl group \(E_{8}\). Zbl 1315.39002
Grammaticos, B.; Ramani, A.
10
2015
Deautonomization by singularity confinement: an algebro-geometric justification. Zbl 1371.39011
Mase, T.; Willox, R.; Grammaticos, B.; Ramani, A.
9
2015
On a novel representation of discrete Painlevé equations. Zbl 1323.39004
Grammaticos, B.; Ramani, A.
8
2015
Discrete Painlevé equations associated with the affine Weyl group \(E_{8}\). Zbl 1326.39006
Ramani, A.; Grammaticos, B.
8
2015
The redemption of singularity confinement. Zbl 1312.37043
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Kanki, M.
7
2015
Singularity confinement and full-deautonomisation: a discrete integrability criterion. Zbl 1364.39001
Grammaticos, B.; Ramani, A.; Willox, R.; Mase, T.; Satsuma, J.
6
2015
Strongly asymmetric discrete Painlevé equations: the additive case. Zbl 1295.39003
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
8
2014
Discrete Painlevé equations with maximal periodicities. Zbl 1301.39005
Ramani, A.; Grammaticos, B.
2
2014
On two discrete Painlevé equations with high periodicities. Zbl 1291.39017
Ramani, A.; Grammaticos, B.
2
2014
Solutions of the lattice sine-Gordon equation and the solitons of its cellular automaton. Zbl 1293.35270
Willox, R.; Ramani, A.; Grammaticos, B.
2
2014
Second-degree Painlevé equations and their contiguity relations. Zbl 1333.34133
Grammaticos, Basil; Ramani, Alfred; Guha, Partha
1
2014
Higher linearizable mappings and their explicit integration. Zbl 1263.39010
Ramani, A.; Grammaticos, B.; Tamizhmani, K. M.; Tamizhmani, T.
2
2013
A new family of discrete Painlevé equations and associated linearisable systems. Zbl 1420.37085
Ramani, A.; Grammaticos, B.
1
2013
Discretising the Painlevé equations à la Hirota-Mickens. Zbl 1274.34261
Grammaticos, B.; Ramani, A.; Satsuma, J.; Willox, R.
6
2012
On the explicit integration of a class of linearizable mappings. Zbl 1253.37068
Ramani, A.; Grammaticos, B.; Satsuma, J.
3
2012
Do ultradiscrete systems with parity variables satisfy the singularity confinement criterion? Zbl 1274.37009
Mimura, N.; Isojima, S.; Murata, M.; Satsuma, J.; Ramani, A.; Grammaticos, B.
1
2012
Linearizable QRT mappings. Zbl 1246.37090
Ramani, A.; Grammaticos, B.; Satsuma, J.; Mimura, N.
11
2011
Generalized QRT mappings with periodic coefficients. Zbl 1210.37039
Ramani, A.; Grammaticos, B.; Willox, R.
5
2011
Mappings of Hirota-Kimura-Yahagi type can have periodic coefficients too. Zbl 1206.39007
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.
4
2011
On two integrable lattice equations and their interpretation. Zbl 1213.37107
Scimiterna, C.; Grammaticos, B.; Ramani, A.
4
2011
On Quispel-Roberts-Thompson extensions and integrable correspondences. Zbl 1317.37056
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Willox, R.
3
2011
Dynamical studies of equations from the Gambier family. Zbl 1220.34059
Guha, Partha; Choudhury, Anindya Ghose; Grammaticos, Basil
2
2011
Painlevé equations: continuous, discrete and ultradiscrete. Zbl 1229.39008
Grammaticos, Basil; Ramani, Alfred
1
2011
Discretising systematically the Painlevé equations. Zbl 1217.37059
Murata, M.; Satsuma, J.; Ramani, A.; Grammaticos, B.
1
2011
Folding transformations and HKY mappings. Zbl 1218.39009
Grammaticos, B.; Ramani, A.; Willox, R.
1
2011
How to discretize differential systems in a systematic way. Zbl 1222.39009
Murata, M.; Satsuma, J.; Ramani, A.; Grammaticos, B.
5
2010
Singularity confinement property for the (non-autonomous) Adler-Bobenko-Suris integrable lattice equations. Zbl 1190.37064
Grammaticos, Basil; Ramani, Alfred
3
2010
Modelling the morphology of migrating bacterial colonies. Zbl 1193.37135
Nishiyama, A.; Tokihiro, T.; Badoual, M.; Grammaticos, B.
2
2010
Solving the ultradiscrete KdV equation. Zbl 1205.35281
Willox, Ralph; Nakata, Yoichi; Satsuma, Junkichi; Ramani, Alfred; Grammaticos, Basile
1
2010
Second-degree discrete Painlevé equations conceal first-degree ones. Zbl 1190.39003
Ramani, A.; Grammaticos, B.; Joshi, N.
1
2010
How to detect the integrability of discrete systems. Zbl 1183.37001
Grammaticos, B.; Halburd, R. G.; Ramani, A.; Viallet, C-M
15
2009
The number of discrete Painlevé equations is infinite. Zbl 1233.34038
Ramani, A.; Grammaticos, B.
7
2009
Modelling the dynamics of nonendemic epidemics. Zbl 1197.92042
Ramani, A.; Grammaticos, B.; Satsuma, J.
4
2009
A discrete-time model for cryptic oscillations in predator-prey systems. Zbl 1186.37107
Willox, R.; Ramani, A.; Grammaticos, B.
4
2009
Investigating the integrability of the Lyness mappings. Zbl 1186.39008
Grammaticos, B.; Ramani, A.; Tamizhmani, T.
2
2009
On the non-autonomous form of the \(Q_4\) mapping and its relation to elliptic Painlevé equations. Zbl 1181.37086
Ramani, A.; Carstea, A. S.; Grammaticos, B.
2
2009
Deautonomizing integrable non-QRT mappings. Zbl 1186.37066
Carstea, A. S.; Grammaticos, B.; Ramani, A.
2
2009
Folding transformations for quantum Painlevé equations. Zbl 1166.34335
Ramani, A.; Nagoya, H.; Grammaticos, B.; Tamizhmani, T.
1
2009
Bilinearization and solutions of the KdV6 equation. Zbl 1155.35440
Ramani, A.; Grammaticos, B.; Willox, R.
9
2008
Quantum Painlevé equations: from continuous to discrete and back. Zbl 1229.34133
Nagoya, H.; Grammaticos, B.; Ramani, A.
3
2008
Quantum Painlevé equations: from continuous to discrete. Zbl 1154.34045
Nagoya, Hajime; Grammaticos, Basil; Ramani, Alfred
1
2008
A class of integrable and nonintegrable mappings and their dynamics. Zbl 1129.37032
Tsuda, Teruhisa; Grammaticos, Basil; Ramani, Alfred; Takenawa, Tomoyuki
12
2007
Constructing lump-like solutions of the Hirota-Miwa equation. Zbl 1155.35462
Grammaticos, B.; Ramani, A.; Papageorgiou, V.; Satsuma, J.; Willox, R.
5
2007
Integrable mappings with transcendental invariants. Zbl 1109.37052
Grammaticos, B.; Ramani, A.
4
2007
Do integrable cellular automata have the confinement property? Zbl 1120.37008
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Carstea, A. S.
3
2007
An (almost) solvable model for bacterial pattern formation. Zbl 1293.92005
Grammaticos, B.; Badoual, M.; Aubert, M.
3
2007
Eigenproblems of large powers of the Laplacian in bounded domains. Zbl 1121.35089
Ramani, A.; Grammaticos, B.; Pomeau, Y.
1
2007
Do all integrable evolution equations have the Painlevé property? Zbl 1135.35306
Tamizhmani, K. M.; Grammaticos, Basil; Ramani, Alfred
1
2007
Deconstructing an integrable lattice equation. Zbl 1086.37037
Ramani, A.; Joshi, N.; Grammaticos, B.; Tamizhmani, T.
11
2006
From integrable lattices to non-QRT mappings. Zbl 1111.39013
Joshi, N.; Grammaticos, B.; Tamizhmani, T.; Ramani, A.
10
2006
Ultradiscretization without positivity. Zbl 1095.93001
Isojima, S.; Grammaticos, B.; Ramani, A.; Satsuma, J.
7
2006
Nonintegrability of \((2+1)\)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis. Zbl 1160.81394
Kumar, C. Senthil; Lakshmanan, M.; Grammaticos, B.; Ramani, A.
6
2006
Discrete systems related to the sixth Painlevé equation. Zbl 1108.39016
Ramani, A.; Ohta, Y.; Grammaticos, B.
3
2006
On the dynamics of a gene regulatory network. Zbl 1099.34050
Grammaticos, B.; Carstea, A. S.; Ramani, A.
3
2006
On the identity of two \(q\)-discrete Painlevé equations and their geometrical derivation. Zbl 1140.39313
Grammaticos, B.; Ramani, A.; Takenawa, T.
1
2006
On the alternate discrete Painlevé equations and related systems. Zbl 1137.39012
Ramani, Alfred; Grammaticos, Basil; Tamizhmani, Thamizharasi
1
2006
Similarity reductions of Hirota bilinear equations and Painlevé equations. Zbl 1123.37030
Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.; Ohta, Y.; Tamizhmani, T.
1
2006
Solvable chaos. Zbl 1369.37046
Grammaticos, B.; Ramani, A.; Viallet, C. M.
12
2005
A study of the antisymmetric QRT mappings. Zbl 1181.37105
Willox, R.; Grammaticos, B.; Ramani, A.
3
2005
On the discrete form of the Fokas–Ablowitz equation. Zbl 1089.39006
Ramani, A.; Grammaticos, B.
2
2005
Generating discrete Painlevé equations from affine Weyl groups. Zbl 1119.39301
Grammaticos, B.; Ramani, A.
2
2005
Discrete Painlevé equations: a review. Zbl 1064.39019
Grammaticos, B.; Ramani, A.
22
2004
On the integrability of correspondences associated to integral curves. Zbl 1118.81454
Viallet, C. M.; Grammaticos, B.; Ramani, A.
12
2004
Discrete integrable systems. Proceedings of the international CIMPA school, Pondicherry, India, February 2–14, 2003. Zbl 1052.37002
Grammaticos, B.; Kosmann-Schwarzbach, Y.; Tamizhmani, T.
11
2004
The \(q\)-discrete Painlevé IV equations and their properties. Zbl 1053.39034
Tamizhmani, K. M.; Grammaticos, B.; Carstea, A. S.; Ramani, A.
5
2004
Special solutions for discrete Painlevé equations. Zbl 1064.39021
Tamizhmani, K. M.; Tamizhmani, T.; Grammaticos, B.; Ramani, A.
2
2004
Modelling AIDS epidemic and treatment with difference equations. Zbl 1068.92030
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.; Carstea, A. S.
2
2004
Integrability of nonlinear systems. Proceedings of the CIMPA school, Pondicherry University, India, January 8–26, 1996. 2nd revised ed. Zbl 1034.93002
Kosmann-Schwarzbach, Y.; Grammaticos, B.; Tamizhmani, K. M.
1
2004
Three lessons on the Painlevé property and the Painlevé equations. Zbl 1073.34099
Kruskal, M. D.; Grammaticos, B.; Tamizhmani, T.
1
2004
Epidemic dynamics: discrete-time and cellular automaton models. Zbl 1026.92042
Willox, R.; Grammaticos, B.; Carstea, A. S.; Ramani, A.
17
2003
The space of initial conditions for linearizable mappings. Zbl 1021.37023
Takenawa, T.; Eguchi, M.; Grammaticos, B.; Ohta, Y.; Ramani, A.; Satsuma, J.
7
2003
A unified description of the asymmetric \(q\text{-P}_{\text{V}}\) and \(d\text{-P}_{\text{IV}}\) equations and their Schlesinger transformations. Zbl 1034.34104
Grammaticos, B.; Ramani, A.; Ohta, Y.
6
2003
The road to the discrete analogue of the Painlevé property: Nevanlinna meets singularity confinement. Zbl 1057.39018
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M.
6
2003
The discrete Painlevé II equations: Miura and auto-Bäcklund transformations. Zbl 1049.39021
Carstea, A. S.; Ramani, A.; Willox, R.; Grammaticos, B.
1
2003
On the autonomous limit of discrete Painlevé equations. Zbl 0992.39015
Ramani, A.; Carstea, A. S.; Grammaticos, B.; Ohta, Y.
19
2002
A new class of integrable discrete systems. Zbl 1042.37012
Kimura, K.; Yahagi, H.; Hirota, R.; Ramani, A.; Grammaticos, B.; Ohta, Y.
13
2002
A bilinear approach to the discrete Painlevé I equations. Zbl 1074.39023
Grammaticos, B.; Tamizhmani, T.; Ramani, A.; Carstea, A. S.; Tamizhmani, K. M.
8
2002
From the continuous P\(_{\text{V}}\) to discrete Painlevé equations. Zbl 1046.39013
Tokihiro, T.; Grammaticos, B.; Ramani, A.
6
2002
Elliptic discrete Painlevé equations. Zbl 1056.39027
Ohta, Y.; Ramani, A.; Grammaticos, B.
6
2002
Linearisable supersymmetric equations. Zbl 1004.34028
Carstea, A. S.; Ramani, A.; Grammaticos, B.
5
2002
The discrete Chazy III system of Labrunie-Conte is not integrable. Zbl 1046.39012
Ramani, A.; Grammaticos, B.; Lafortune, S.
2
2002
A panorama of the special solutions of the Painlevé equations. Zbl 1057.39019
Tamizhmani, K. M.; Grammaticos, B.; Tamizhmani, T.; Ramani, A.
1
2002
On discrete Painlevé equations associated with the lattice KdV systems and the Painlevé VI equation. Zbl 1152.39313
Nijhoff, F. W.; Ramani, A.; Grammaticos, B.; Ohta, Y.
19
2001
An affine Weyl group approach to the eight-parameter discrete Painlevé equation. Zbl 1002.39029
Ohta, Y.; Ramani, A.; Grammaticos, B.
18
2001
Integrable lattice equations and their growth properties. Zbl 1072.37509
Tremblay, S.; Grammaticos, B.; Ramani, A.
16
2001
...and 104 more Documents
all top 5

Cited by 939 Authors

83 Grammaticos, Basil
79 Ramani, Alfred
24 Tamizhmani, K. M.
23 Ma, Wen-Xiu
19 Joshi, Nalini
18 Winternitz, Pavel
17 Clarkson, Peter A.
17 Sahadevan, Ramajayam
16 Satsuma, Junkichi
15 Ohta, Yasuhiro
14 Hu, Xingbiao
14 Tamizhmani, Thamizharasi
14 Willox, Ralph
13 Llibre, Jaume
11 Van Assche, Walter
10 Cârstea, Adrian Ştefan
10 Gubbiotti, Giorgio
10 He, Yi
10 Korhonen, Risto
10 Mase, Takafumi
10 Nijhoff, Frank W.
9 Conte, Robert M.
9 Tokihiro, Tetsuji
8 Chang, Xiangke
8 Dorizzi, Bernadette
8 Guha, Partha
8 Kajiwara, Kenji
8 Leach, Peter Gavin Lawrence
8 Pickering, Andrew
8 Scimiterna, Christian
8 Teng, Zhi-dong
8 Tsuda, Teruhisa
8 Zhang, Dajun
7 Gordoa, Pilar Ruiz
7 Hone, Andrew N. W.
7 Kanki, Masataka
7 Levi, Decio
7 Musette, Micheline
7 Viallet, Claude Michel
6 Akylas, T. R.
6 Ghose Choudhury, Anindya
6 Hietarinta, Jarmo
6 Lou, Senyue
6 Mañosa, Víctor
6 Papageorgiou, Vassilios G.
6 Sun, Jianqing
6 Takahashi, Daisuke A.
6 Takenawa, Tomoyuki
6 Valls Anglés, Cláudia
6 Zhang, Yi
5 Filipuk, Galina V.
5 Grimshaw, Roger Hamilton James
5 Hu, Zengyun
5 Isojima, Shin
5 Marchesiello, Antonella
5 Moulin Ollagnier, Jean
5 Murata, Mikio
5 Nagoya, Hajime
5 Nakazono, Nobutaka
5 Quispel, Gilles Reinout Willem
5 Roberts, John Anthony Gerard
5 Šnobl, Libor
5 Suris, Yuri Borisovich
5 Tsujimoto, Satoshi
5 van der Kamp, Peter H.
5 Yoshida, Haruo
4 Adler, Vsevolod Eduardovich
4 Bountis, Tassos C.
4 Brezinski, Claude
4 Chen, Zongxuan
4 Cima, Anna
4 Cui, Shangbin
4 Daripa, Prabir K.
4 Fordy, Allan P.
4 Gao, Yitian
4 Goriely, Alain
4 Halburd, Rodney G.
4 Il’ichev, Andreĭ Teĭmurazovich
4 Ishizaki, Katsuya
4 Kamiya, Ryo
4 Lafortune, Stéphane
4 Lesfari, Ahmed
4 Liu, Yinping
4 Lustri, Christopher J.
4 Mansfield, Elizabeth Louise
4 Maruno, Kenichi
4 Nagao, Hidehito
4 Nishioka, Seiji
4 Popovych, Roman O.
4 Pucacco, Giuseppe
4 Rañada, Manuel F.
4 Sakai, Hidetaka
4 Schief, Wolfgang Karl
4 Shi, Yang
4 Tsyganov, Andreĭ Vladimirovich
4 van Gorder, Robert Ashton
4 Witte, Nicholas S.
4 Xenitidis, Pavlos
4 Yamada, Yasuhiko
4 Yehia, Hamad M.
...and 839 more Authors
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Cited in 198 Serials

150 Journal of Mathematical Physics
51 Journal of Nonlinear Mathematical Physics
32 Physica D
30 Physics Letters. A
30 Chaos, Solitons and Fractals
29 Applied Mathematics and Computation
23 Journal of Physics A: Mathematical and Theoretical
22 Journal of Mathematical Analysis and Applications
22 Theoretical and Mathematical Physics
20 Letters in Mathematical Physics
19 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
16 Studies in Applied Mathematics
16 Journal of Difference Equations and Applications
15 Computers & Mathematics with Applications
12 Advances in Difference Equations
11 Communications in Mathematical Physics
11 Communications in Nonlinear Science and Numerical Simulation
10 Journal of Geometry and Physics
10 Acta Applicandae Mathematicae
9 Physica A
8 Journal of Differential Equations
8 Proceedings of the American Mathematical Society
8 Celestial Mechanics and Dynamical Astronomy
8 Regular and Chaotic Dynamics
7 Applied Mathematics Letters
6 Mathematics and Computers in Simulation
6 Nonlinear Dynamics
5 Computer Physics Communications
5 Journal of Computational and Applied Mathematics
5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
5 Abstract and Applied Analysis
5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
4 Applicable Analysis
4 Mathematical Methods in the Applied Sciences
4 Nonlinearity
4 Journal of Approximation Theory
4 Japan Journal of Industrial and Applied Mathematics
4 Numerical Algorithms
4 Chaos
4 Acta Mathematica Sinica. English Series
4 Journal of High Energy Physics
4 Qualitative Theory of Dynamical Systems
4 Physical Review Letters
4 Nonlinear Analysis. Real World Applications
4 Computational Methods and Function Theory
4 International Journal of Geometric Methods in Modern Physics
4 Frontiers of Mathematics in China
4 Advances in Mathematical Physics
4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
3 Modern Physics Letters A
3 Bulletin of the Australian Mathematical Society
3 International Journal of Theoretical Physics
3 Journal of Fluid Mechanics
3 Wave Motion
3 Mathematics of Computation
3 Reviews in Mathematical Physics
3 Functional Analysis and its Applications
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Siberian Mathematical Journal
3 Transactions of the American Mathematical Society
3 Advances in Applied Mathematics
3 Constructive Approximation
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Mathematical Problems in Engineering
3 Communications in Theoretical Physics
3 Science China. Mathematics
3 Ufimskiĭ Matematicheskiĭ Zhurnal
3 Analysis and Mathematical Physics
3 Journal of Computational Dynamics
2 Modern Physics Letters B
2 International Journal of Modern Physics A
2 Acta Mechanica
2 Indian Journal of Pure & Applied Mathematics
2 Mathematical Notes
2 Reports on Mathematical Physics
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Physics of Fluids, A
2 Duke Mathematical Journal
2 Nagoya Mathematical Journal
2 Theoretical Computer Science
2 Ergodic Theory and Dynamical Systems
2 Journal of Scientific Computing
2 Aequationes Mathematicae
2 Annals of Physics
2 Applied Mathematical Modelling
2 International Journal of Computer Mathematics
2 Journal of Algebraic Combinatorics
2 Journal of Mathematical Sciences (New York)
2 Bulletin des Sciences Mathématiques
2 Complexity
2 Discrete and Continuous Dynamical Systems
2 The Ramanujan Journal
2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 Discrete Dynamics in Nature and Society
2 Annales Henri Poincaré
2 International Journal of Nonlinear Sciences and Numerical Simulation
2 The ANZIAM Journal
2 Dynamical Systems
2 Discrete and Continuous Dynamical Systems. Series B
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
...and 98 more Serials
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Cited in 50 Fields

469 Dynamical systems and ergodic theory (37-XX)
284 Partial differential equations (35-XX)
254 Difference and functional equations (39-XX)
233 Ordinary differential equations (34-XX)
98 Mechanics of particles and systems (70-XX)
73 Special functions (33-XX)
60 Quantum theory (81-XX)
58 Numerical analysis (65-XX)
45 Fluid mechanics (76-XX)
43 Algebraic geometry (14-XX)
33 Biology and other natural sciences (92-XX)
32 Functions of a complex variable (30-XX)
24 Nonassociative rings and algebras (17-XX)
24 Global analysis, analysis on manifolds (58-XX)
23 Computer science (68-XX)
20 Differential geometry (53-XX)
20 Statistical mechanics, structure of matter (82-XX)
13 Harmonic analysis on Euclidean spaces (42-XX)
10 Number theory (11-XX)
9 Field theory and polynomials (12-XX)
9 Linear and multilinear algebra; matrix theory (15-XX)
9 Optics, electromagnetic theory (78-XX)
9 Relativity and gravitational theory (83-XX)
8 Commutative algebra (13-XX)
8 Associative rings and algebras (16-XX)
8 Approximations and expansions (41-XX)
8 Systems theory; control (93-XX)
7 Information and communication theory, circuits (94-XX)
6 Combinatorics (05-XX)
6 Geometry (51-XX)
5 Several complex variables and analytic spaces (32-XX)
5 Integral equations (45-XX)
4 Probability theory and stochastic processes (60-XX)
4 Mechanics of deformable solids (74-XX)
3 Topological groups, Lie groups (22-XX)
3 Operator theory (47-XX)
2 General and overarching topics; collections (00-XX)
2 History and biography (01-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Group theory and generalizations (20-XX)
2 Measure and integration (28-XX)
2 Integral transforms, operational calculus (44-XX)
2 Functional analysis (46-XX)
1 Real functions (26-XX)
1 Potential theory (31-XX)
1 Abstract harmonic analysis (43-XX)
1 Convex and discrete geometry (52-XX)
1 General topology (54-XX)
1 Manifolds and cell complexes (57-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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