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Author ID: ramani.alfred Recent zbMATH articles by "Ramani, Alfred"
Published as: Ramani, A.; Ramani, Alfred
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Publications by Year

Citations contained in zbMATH Open

214 Publications have been cited 2,965 times in 1,567 Documents Cited by Year
A connection between nonlinear evolution equations and ordinary differential equations of P-type. I. Zbl 0445.35056
Ablowitz, M. J.; Ramani, A.; Segur, H.
329
1980
Do integrable mappings have the Painlevé property? Zbl 0990.37518
Grammaticos, B.; Ramani, A.; Papageorgiou, V.
189
1991
Discrete versions of the Painlevé equations. Zbl 1050.39500
Ramani, A.; Grammaticos, B.; Hietarinta, J.
158
1991
A connection between nonlinear evolution equations and ordinary differential equations of P-type. II. Zbl 0445.35057
Ablowitz, M. J.; Ramani, A.; Segur, H.
128
1980
Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable? Zbl 0619.35086
Dorizzi, B.; Grammaticos, B.; Ramani, A.; Winternitz, P.
89
1986
Structural stability of the Korteweg-de Vries solitons under a singular perturbation. Zbl 0695.35161
Pomeau, Y.; Ramani, A.; Grammaticos, B.
85
1988
From continuous to discrete Painlevé equations. Zbl 0794.34013
Fokas, A. S.; Grammaticos, B.; Ramani, A.
66
1993
Discrete Painlevé equations: coalescences, limits and degeneracies. Zbl 0912.34011
Ramani, A.; Grammaticos, B.
64
1996
Integrable Hamiltonian systems with velocity-dependent potentials. Zbl 0586.70013
Dorizzi, B.; Grammaticos, B.; Ramani, A.; Winternitz, P.
44
1985
Integrability of Hamiltonians with third- and fourth-degree polynomial potentials. Zbl 0547.70017
Grammaticos, B.; Dorizzi, B.; Ramani, Alfred
44
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.
42
1990
On the complete and partial integrability of non-Hamiltonian systems. Zbl 0599.34002
Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.
37
1984
Discrete Painlevé equations. Zbl 1014.39013
Grammaticos, Basile; Nijhoff, Frank W.; Ramani, Alfred
36
1999
Discrete Painlevé equations: a review. Zbl 1064.39019
Grammaticos, B.; Ramani, A.
33
2004
Integrable lattices and convergence acceleration algorithms. Zbl 0910.65001
Papageorgiou, V.; Grammaticos, B.; Ramani, A.
32
1993
Soliton structure of the Drinfel’d-Sokolov-Wilson equation. Zbl 0638.35071
Hirota, R.; Grammaticos, B.; Ramani, A.
28
1986
Hamiltonians with high-order integrals and the ”weak-Painlevé” concept. Zbl 0549.70009
Grammaticos, B.; Dorizzi, B.; Ramani, A.
27
1984
Epidemic dynamics: discrete-time and cellular automaton models. Zbl 1026.92042
Willox, R.; Grammaticos, B.; Carstea, A. S.; Ramani, A.
27
2003
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.
26
2001
On the autonomous limit of discrete Painlevé equations. Zbl 0992.39015
Ramani, A.; Carstea, A. S.; Grammaticos, B.; Ohta, Y.
25
2002
An affine Weyl group approach to the eight-parameter discrete Painlevé equation. Zbl 1002.39029
Ohta, Y.; Ramani, A.; Grammaticos, B.
25
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.
24
1995
Inverse scattering, ordinary differential equations of Painlevé-type, and Hirota’s bilinear formalism. Zbl 0599.47017
Ramani, A.
23
1981
How to detect the integrability of discrete systems. Zbl 1183.37001
Grammaticos, B.; Halburd, R. G.; Ramani, A.; Viallet, C-M
23
2009
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
Miura transforms for discrete Painlevé equations. Zbl 0754.35149
Ramani, A.; Grammaticos, B.
22
1992
Integrable lattice equations and their growth properties. Zbl 1072.37509
Tremblay, S.; Grammaticos, B.; Ramani, A.
22
2001
A study of the alternate discrete Painlevé II equation. Zbl 0860.35124
Nijhoff, F.; Satsuma, J.; Kajiwara, K.; Grammaticos, B.; Ramani, A.
22
1996
Bilinear discrete Painlevé equations. Zbl 0867.39001
Ramani, A.; Grammaticos, B.; Satsuma, J.
22
1995
Constructing the soliton solutions for the \(N=1\) supersymmetric KdV hierarchy. Zbl 1067.37107
Carstea, A. S.; Ramani, A.; Grammaticos, B.
21
2001
The Gambier mapping, revisited. Zbl 0910.58017
Grammaticos, B.; Ramani, A.; Lafortune, S.
20
1998
Asymmetric discrete Painlevé equations. Zbl 0983.34083
Kruskal, M. D.; Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.
20
2000
On a novel \(q\)-discrete analogue of the Painlevé VI equation. Zbl 0938.39020
Grammaticos, B.; Ramani, A.
19
1999
Degeneration through coalescence of the \(q\)-Painlevé VI equation. Zbl 0932.39017
Grammaticos, B.; Ohta, Y.; Ramani, A.; Sakai, H.
19
1998
Special function solutions of the discrete Painlevé equations. Zbl 0994.33500
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M.
18
2001
Lie symmetries of Hirota’s bilinear equations. Zbl 0737.35110
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.
18
1991
The mixmaster universe model, revisited. Zbl 0844.58120
Contopoulos, G.; Grammaticos, B.; Ramani, A.
17
1994
Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations. Zbl 0939.37041
Ohta, Y.; Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.
17
1999
Delay-differential equations and the Painlevé transcendents. Zbl 0803.34008
Grammaticos, B.; Ramani, A.; Moreira, I. C.
17
1993
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.
16
1998
Linearizable mappings and the low-growth criterion. Zbl 0962.37020
Ramani, A.; Grammaticos, B.; Lafortune, S.; Ohta, Y.
16
2000
On the integrability of correspondences associated to integral curves. Zbl 1118.81454
Viallet, C. M.; Grammaticos, B.; Ramani, A.
15
2004
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.
15
1996
Integrable systems without the Painlevé property. Zbl 0953.34077
Ramani, A.; Grammaticos, B.; Tremblay, S.
15
2000
A new class of integrable discrete systems. Zbl 1042.37012
Kimura, K.; Yahagi, H.; Hirota, R.; Ramani, A.; Grammaticos, B.; Ohta, Y.
15
2002
From continuous Painlevé IV to the asymmetric discrete Painlevé. I. Zbl 0910.34019
Grammaticos, B.; Ramani, A.
15
1998
Solvable chaos. Zbl 1369.37046
Grammaticos, B.; Ramani, A.; Viallet, C. M.
14
2005
On a transcendental equation related to Painlevé III, and its discrete forms. Zbl 0948.34070
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M.
14
2000
Explicit integrability for Hamiltonian systems and the Painlevé conjecture. Zbl 0566.70020
Dorizzi, B.; Grammaticos, B.; Ramani, A.
14
1984
Bilinearization and soliton solutions of the \(N=1\) supersymmetric sine-Gordon equation. Zbl 0980.35147
Grammaticos, B.; Ramani, A.; Carstea, A. S.
14
2001
Painlevé analysis and singularity confinement: The ultimate conjecture. Zbl 0773.35076
Ramani, A.; Grammaticos, B.; Tamizhmani, K. M.
14
1993
A class of integrable and nonintegrable mappings and their dynamics. Zbl 1129.37032
Tsuda, Teruhisa; Grammaticos, Basil; Ramani, Alfred; Takenawa, Tomoyuki
13
2007
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.
13
1985
A search for integrable bilinear equations: The Painlevé approach. Zbl 0729.35133
Grammaticos, B.; Ramani, A.; Hietarinta, J.
13
1990
Growth and integrability in discrete systems. Zbl 1006.39018
Grammaticos, B.; Tamizhmani, T.; Ramani, A.; Tamizhmani, K. M.
13
2001
The hunting for the discrete Painlevé equations. Zbl 0951.39005
Grammaticos, B.; Ramani, A.
13
2000
Painlevé analysis for the mixmaster universe model. Zbl 0811.53086
Contopoulos, G.; Grammaticos, B.; Ramani, A.
13
1993
Quadratic relations in continuous and discrete Painlevé equations. Zbl 0953.34078
Ramani, A.; Grammaticos, B.; Tamizhmani, T.
13
2000
An integrability test for differential-difference systems. Zbl 0757.34057
Ramani, A.; Grammaticos, B.; Tamizhmani, K. M.
13
1992
The redemption of singularity confinement. Zbl 1312.37043
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Kanki, M.
13
2015
On the non-integrability of some generalized Toda lattices. Zbl 0667.58021
Yoshida, H.; Ramani, A.; Grammaticos, B.; Hietarinta, J.
13
1987
Linearizable QRT mappings. Zbl 1246.37090
Ramani, A.; Grammaticos, B.; Satsuma, J.; Mimura, N.
13
2011
Casorati determinant solutions for the discrete Painlevé-II equation. Zbl 0811.35150
Kajiwara, Kenji; Ohta, Yasuhiro; Satsuma, Junkichi; Grammaticos, Basil; Ramani, Alfred
12
1994
Generalized separability for a Hamiltonian with nonseparable quartic potential. Zbl 0961.70502
Ravoson, V.; Ramani, A.; Grammaticos, B.
12
1994
Linearization and solutions of the discrete Painlevé III equation. Zbl 0941.34502
Grammaticos, B.; Nijhoff, F. W.; Papageorgiou, V.; Ramani, A.; Satsuma, J.
12
1994
Discrete integrable systems from continuous Painlevé equations through limiting procedures. Zbl 0963.37069
Ramani, A.; Ohta, Y.; Grammaticos, B.
12
2000
Singularity analysis for difference Painlevé equations associated with the affine Weyl group \(E_8\). Zbl 1359.39005
Ramani, A.; Grammaticos, B.
12
2017
Integrability of Klein-Gordon equations. Zbl 0629.35104
Clarkson, Peter A.; McLeod, J. Bryce; Olver, Peter J.; Ramani, Alfred
11
1986
From integrable lattices to non-QRT mappings. Zbl 1111.39013
Joshi, N.; Grammaticos, B.; Tamizhmani, T.; Ramani, A.
11
2006
Discrete Painlevé equations: Derivation and properties. Zbl 0793.35093
Grammaticos, B.; Ramani, A.
11
1993
Linearization and solutions of the discrete Painlevé III equation. Zbl 0909.39004
Grammaticos, B.; Nijhoff, F. W.; Papageorgiou, V.; Ramani, A.; Satsuma, J.
11
1994
Deconstructing an integrable lattice equation. Zbl 1086.37037
Ramani, A.; Joshi, N.; Grammaticos, B.; Tamizhmani, T.
11
2006
Constructing solutions to the ultradiscrete Painlevé equations. Zbl 0926.39007
Takahashi, D.; Tokihiro, T.; Grammaticos, B.; Ohta, Y.; Ramani, A.
11
1997
Elliptic and multiplicative discrete Painlevé equations from the affine Weyl group \(E_{8}\). Zbl 1315.39002
Grammaticos, B.; Ramani, A.
11
2015
Deautonomization by singularity confinement: an algebro-geometric justification. Zbl 1371.39011
Mase, T.; Willox, R.; Grammaticos, B.; Ramani, A.
11
2015
Non-integrability of the fourth-order truncated Toda Hamiltonian. Zbl 0656.58014
Yoshida, H.; Ramani, A.; Grammaticos, B.
10
1988
A bilinear approach to discrete Miura transformations. Zbl 1044.37547
Joshi, N.; Ramani, A.; Grammaticos, B.
10
1998
A bilinear approach to the discrete Painlevé I equations. Zbl 1074.39023
Grammaticos, B.; Tamizhmani, T.; Ramani, A.; Carstea, A. S.; Tamizhmani, K. M.
10
2002
Multilinear operators: The natural extension of Hirota’s bilinear formalism. Zbl 0961.35503
Grammaticos, B.; Ramani, A.; Hietarinta, J.
10
1994
Elliptic discrete Painlevé equations. Zbl 1056.39027
Ohta, Y.; Ramani, A.; Grammaticos, B.
10
2002
The space of initial conditions for linearizable mappings. Zbl 1021.37023
Takenawa, T.; Eguchi, M.; Grammaticos, B.; Ohta, Y.; Ramani, A.; Satsuma, J.
10
2003
Integrability – and how to detect it. Zbl 0904.58028
Grammaticos, B.; Ramani, A.
10
1997
Coalescence cascades and special-function solutions for the continuous and discrete Painlevé equations. Zbl 0910.34020
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.; Kajiwara, K.
10
1998
Retracing the Painlevé-Gambier classification for discrete systems. Zbl 0896.35122
Grammaticos, B.; Ramani, A.
10
1997
Bilinear discrete Painlevé-II and its particular solutions. Zbl 0859.34073
Satsuma, J.; Kajiwara, K.; Grammaticos, B.; Hietarinta, J.; Ramani, A.
10
1995
Ultradiscretization without positivity. Zbl 1095.93001
Isojima, S.; Grammaticos, B.; Ramani, A.; Satsuma, J.
10
2006
Bilinearization and solutions of the KdV6 equation. Zbl 1155.35440
Ramani, A.; Grammaticos, B.; Willox, R.
9
2008
Schlesinger transforms for the discrete Painlevé IV equation. Zbl 0789.39001
Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.
9
1993
The Gambier mapping. Zbl 0909.39005
Grammaticos, B.; Ramani, A.
9
1996
Calculating algebraic entropies: an express method. Zbl 1390.81106
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.
9
2017
Nonintegrability of \((2+1)\)-dimensional continuum isotropic Heisenberg spin system: Painlevé analysis. Zbl 1160.81394
Kumar, C. Senthil; Lakshmanan, M.; Grammaticos, B.; Ramani, A.
9
2006
Discretising the Painlevé equations à la Hirota-Mickens. Zbl 1274.34261
Grammaticos, B.; Ramani, A.; Satsuma, J.; Willox, R.
9
2012
Singularity analysis and its relation to complete, partial and non- integrability. Zbl 0715.58017
Kruskal, M. D.; Ramani, A.; Grammaticos, B.
8
1990
Singularity structure and algebraic properties of the differential-difference Kadomtsev-Petviashvili equation. Zbl 1121.37318
Tamizhmani, K. M.; Kanagavel, S.; Grammaticos, B.; Ramani, A.
8
2000
Integrability and the Painlevé property for low-dimensional systems. Zbl 0553.34032
Ramani, A.; Dorizzi, B.; Grammaticos, B.; Bountis, T.
8
1984
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.
8
2003
Singularity confinement and full-deautonomisation: a discrete integrability criterion. Zbl 1364.39001
Grammaticos, B.; Ramani, A.; Willox, R.; Mase, T.; Satsuma, J.
8
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
Strongly asymmetric discrete Painlevé equations: the additive case. Zbl 1295.39003
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
8
2014
On the singularities of the discrete Korteweg-deVries equation. Zbl 1519.37102
Um, D.; Ramani, A.; Grammaticos, B.; Willox, R.; Satsuma, J.
2
2021
On the singularity structure of the discrete KdV equation. Zbl 1514.39012
Um, Doyong; Willox, Ralph; Grammaticos, Basil; Ramani, Alfred
4
2020
Discrete Painlevé equations from singularity patterns: the asymmetric trihomographic case. Zbl 1441.39013
Grammaticos, B.; Ramani, A.; Willox, R.; Satsuma, J.
1
2020
Singularity confinement as an integrability criterion. Zbl 1509.39014
Mase, Takafumi; Willox, Ralph; Ramani, Alfred; Grammaticos, Basil
4
2019
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
Integrable mappings and the notion of anticonfinement. Zbl 1405.37063
Mase, T.; Willox, R.; Ramani, A.; Grammaticos, B.
6
2018
On the canonical forms of QRT mappings and discrete Painlevé equations. Zbl 1406.39007
Ramani, A.; Grammaticos, B.; Satsuma, J.; Tamizhmani, T.
4
2018
Calculating the algebraic entropy of mappings with unconfined singularities. Zbl 1397.37062
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Satsuma, J.
3
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.
12
2017
Calculating algebraic entropies: an express method. Zbl 1390.81106
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.
9
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.
5
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
Multiplicative equations related to the affine Weyl group \(\mathrm{E}_8\). Zbl 1373.39005
Grammaticos, B.; Ramani, A.; Willox, R.; Satsuma, J.
1
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.
2
2016
The redemption of singularity confinement. Zbl 1312.37043
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Kanki, M.
13
2015
Elliptic and multiplicative discrete Painlevé equations from the affine Weyl group \(E_{8}\). Zbl 1315.39002
Grammaticos, B.; Ramani, A.
11
2015
Deautonomization by singularity confinement: an algebro-geometric justification. Zbl 1371.39011
Mase, T.; Willox, R.; Grammaticos, B.; Ramani, A.
11
2015
Singularity confinement and full-deautonomisation: a discrete integrability criterion. Zbl 1364.39001
Grammaticos, B.; Ramani, A.; Willox, R.; Mase, T.; Satsuma, J.
8
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
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.
3
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
On two discrete Painlevé equations with high periodicities. Zbl 1291.39017
Ramani, A.; Grammaticos, B.
2
2014
Second-degree Painlevé equations and their contiguity relations. Zbl 1333.34133
Grammaticos, Basil; Ramani, Alfred; Guha, Partha
2
2014
A new family of discrete Painlevé equations and associated linearisable systems. Zbl 1420.37085
Ramani, A.; Grammaticos, B.
4
2013
Higher linearizable mappings and their explicit integration. Zbl 1263.39010
Ramani, A.; Grammaticos, B.; Tamizhmani, K. M.; Tamizhmani, T.
2
2013
Contiguity relations for linearisable systems of Gambier type. Zbl 1420.37086
Ramani, A.; Grammaticos, B.; Guha, P.
1
2013
Discretising the Painlevé equations à la Hirota-Mickens. Zbl 1274.34261
Grammaticos, B.; Ramani, A.; Satsuma, J.; Willox, R.
9
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.
2
2012
Linearizable QRT mappings. Zbl 1246.37090
Ramani, A.; Grammaticos, B.; Satsuma, J.; Mimura, N.
13
2011
Generalized QRT mappings with periodic coefficients. Zbl 1210.37039
Ramani, A.; Grammaticos, B.; Willox, R.
7
2011
On two integrable lattice equations and their interpretation. Zbl 1213.37107
Scimiterna, C.; Grammaticos, B.; Ramani, A.
4
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 Quispel-Roberts-Thompson extensions and integrable correspondences. Zbl 1317.37056
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Willox, R.
3
2011
Folding transformations and HKY mappings. Zbl 1218.39009
Grammaticos, B.; Ramani, A.; Willox, R.
1
2011
Miura transformations and the various guises of integrable lattice equations. Zbl 1220.34009
Grammaticos, B.; Ramani, A.; Scimiterna, C.; Willox, R.
1
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
How to discretize differential systems in a systematic way. Zbl 1222.39009
Murata, M.; Satsuma, J.; Ramani, A.; Grammaticos, B.
7
2010
Singularity confinement property for the (non-autonomous) Adler-Bobenko-Suris integrable lattice equations. Zbl 1190.37064
Grammaticos, Basil; Ramani, Alfred
5
2010
Solving the ultradiscrete KdV equation. Zbl 1205.35281
Willox, Ralph; Nakata, Yoichi; Satsuma, Junkichi; Ramani, Alfred; Grammaticos, Basile
5
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
23
2009
A discrete-time model for cryptic oscillations in predator-prey systems. Zbl 1186.37107
Willox, R.; Ramani, A.; Grammaticos, B.
7
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
Deautonomizing integrable non-QRT mappings. Zbl 1186.37066
Carstea, A. S.; Grammaticos, B.; Ramani, A.
3
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.
3
2009
Investigating the integrability of the Lyness mappings. Zbl 1186.39008
Grammaticos, B.; Ramani, A.; Tamizhmani, T.
2
2009
On two (not so) new integrable partial difference equations. Zbl 1172.35509
Ramani, A.; Grammaticos, B.; Satsuma, J.; Willox, R.
2
2009
Folding transformations for quantum Painlevé equations. Zbl 1166.34335
Ramani, A.; Nagoya, H.; Grammaticos, B.; Tamizhmani, T.
1
2009
Hirota bilinear formalism and ultra-discrete singularity analysis. Zbl 1172.39021
Joshi, N.; Lafortune, S.; Ramani, A.
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. Zbl 1154.34045
Nagoya, Hajime; Grammaticos, Basil; Ramani, Alfred
3
2008
Quantum Painlevé equations: from continuous to discrete and back. Zbl 1229.34133
Nagoya, H.; Grammaticos, B.; Ramani, A.
3
2008
Discretization-induced delays and their role in the dynamics. Zbl 1144.82351
Ramani, A.; Grammaticos, B.; Satsuma, J.; Willox, R.
2
2008
Painlevé equations: from continuous to discrete. Zbl 1190.34117
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.; Tamizhmani, T.
1
2008
A class of integrable and nonintegrable mappings and their dynamics. Zbl 1129.37032
Tsuda, Teruhisa; Grammaticos, Basil; Ramani, Alfred; Takenawa, Tomoyuki
13
2007
Constructing lump-like solutions of the Hirota-Miwa equation. Zbl 1155.35462
Grammaticos, B.; Ramani, A.; Papageorgiou, V.; Satsuma, J.; Willox, R.
6
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.
4
2007
Do all integrable evolution equations have the Painlevé property? Zbl 1135.35306
Tamizhmani, K. M.; Grammaticos, Basil; Ramani, Alfred
1
2007
Eigenproblems of large powers of the Laplacian in bounded domains. Zbl 1121.35089
Ramani, A.; Grammaticos, B.; Pomeau, Y.
1
2007
From integrable lattices to non-QRT mappings. Zbl 1111.39013
Joshi, N.; Grammaticos, B.; Tamizhmani, T.; Ramani, A.
11
2006
Deconstructing an integrable lattice equation. Zbl 1086.37037
Ramani, A.; Joshi, N.; Grammaticos, B.; Tamizhmani, T.
11
2006
Ultradiscretization without positivity. Zbl 1095.93001
Isojima, S.; Grammaticos, B.; Ramani, A.; Satsuma, J.
10
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.
9
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
Similarity reductions of Hirota bilinear equations and Painlevé equations. Zbl 1123.37030
Tamizhmani, K. M.; Grammaticos, B.; Ramani, A.; Ohta, Y.; Tamizhmani, T.
2
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
Bilinear avatars of the discrete Painlevé II equation. Zbl 1126.39015
Grammaticos, B.; Ramani, A.; Carstea, A. S.
1
2006
Solvable chaos. Zbl 1369.37046
Grammaticos, B.; Ramani, A.; Viallet, C. M.
14
2005
Generating discrete Painlevé equations from affine Weyl groups. Zbl 1119.39301
Grammaticos, B.; Ramani, A.
3
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
Discrete Painlevé equations: a review. Zbl 1064.39019
Grammaticos, B.; Ramani, A.
33
2004
On the integrability of correspondences associated to integral curves. Zbl 1118.81454
Viallet, C. M.; Grammaticos, B.; Ramani, A.
15
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
Modelling AIDS epidemic and treatment with difference equations. Zbl 1068.92030
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.; Carstea, A. S.
2
2004
Special solutions for discrete Painlevé equations. Zbl 1064.39021
Tamizhmani, K. M.; Tamizhmani, T.; Grammaticos, B.; Ramani, A.
2
2004
Epidemic dynamics: discrete-time and cellular automaton models. Zbl 1026.92042
Willox, R.; Grammaticos, B.; Carstea, A. S.; Ramani, A.
27
2003
The space of initial conditions for linearizable mappings. Zbl 1021.37023
Takenawa, T.; Eguchi, M.; Grammaticos, B.; Ohta, Y.; Ramani, A.; Satsuma, J.
10
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.
8
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.
7
2003
The discrete Painlevé II equations: Miura and auto-Bäcklund transformations. Zbl 1049.39021
Carstea, A. S.; Ramani, A.; Willox, R.; Grammaticos, B.
3
2003
On the autonomous limit of discrete Painlevé equations. Zbl 0992.39015
Ramani, A.; Carstea, A. S.; Grammaticos, B.; Ohta, Y.
25
2002
A new class of integrable discrete systems. Zbl 1042.37012
Kimura, K.; Yahagi, H.; Hirota, R.; Ramani, A.; Grammaticos, B.; Ohta, Y.
15
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.
10
2002
Elliptic discrete Painlevé equations. Zbl 1056.39027
Ohta, Y.; Ramani, A.; Grammaticos, B.
10
2002
From the continuous P\(_{\text{V}}\) to discrete Painlevé equations. Zbl 1046.39013
Tokihiro, T.; Grammaticos, B.; Ramani, A.
7
2002
...and 114 more Documents
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Cited by 1,557 Authors

116 Grammaticos, Basil
111 Ramani, Alfred
37 Winternitz, Pavel
31 Ma, Wen-Xiu
28 Joshi, Nalini
27 Tamizhmani, K. M.
26 Clarkson, Peter A.
24 Kudryashov, Nikolaĭ Alekseevich
23 Sahadevan, Ramajayam
22 Willox, Ralph
21 Satsuma, Junkichi
20 Hu, Xingbiao
19 Llibre, Jaume
19 Pickering, Andrew
16 Cârstea, Adrian Ştefan
16 Kajiwara, Kenji
15 Gordoa, Pilar Ruiz
15 Leach, Peter Gavin Lawrence
15 Ohta, Yasuhiro
15 Tamizhmani, Thamizharasi
14 Conte, Robert Maurice
14 Gubbiotti, Giorgio
14 Nijhoff, Frank W.
13 Korhonen, Risto
13 Lakshmanan, Muthusamy
13 Mase, Takafumi
13 Porsezian, Kuppusamy
12 Chang, Xiangke
12 He, Yi
11 Dorizzi, Bernadette
11 Hietarinta, Jarmo
11 Hone, Andrew N. W.
11 Lou, Senyue
11 Šnobl, Libor
11 Van Assche, Walter
10 Guha, Partha
10 Musette, Micheline
10 Nakazono, Nobutaka
10 Paliathanasis, Andronikos
10 Papageorgiou, Vassilios G.
10 Tam, Hon-Wah
10 Tian, Bo
10 Tokihiro, Tetsuji
9 Bountis, Tassos C.
9 Quispel, Gilles Reinout Willem
9 Takenawa, Tomoyuki
9 Teng, Zhi-dong
9 Viallet, Claude Michel
9 Yamada, Yasuhiko
9 Zhang, Dajun
9 Zhang, Hongqing
8 Alagesan, Thangavel
8 Gao, Yitian
8 Isojima, Shin
8 Kanki, Masataka
8 Levi, Decio
8 Scimiterna, Christian
8 Takahashi, Daisuke A.
8 Tsuda, Teruhisa
8 Valls Anglés, Cláudia
8 Zhang, Yi
8 Zhu, Zuonong
7 Ablowitz, Mark Jay
7 Doikou, Anastasia
7 Doliwa, Adam
7 Filipuk, Galina V.
7 Grimshaw, Roger Hamilton James
7 Maruno, Kenichi
7 Sakovich, Sergei Yu.
7 Tabor, Michael
7 Tsujimoto, Satoshi
6 Akylas, T. R.
6 Capel, Hans W.
6 Chen, Yong
6 Fordy, Allan P.
6 Ghose Choudhury, Anindya
6 Goriely, Alain
6 Grundland, Alfred Michel
6 Hu, Zengyun
6 Lafortune, Stéphane
6 Li, Zhibin
6 Lin, Ji
6 Lustri, Christopher J.
6 Maciejewski, Andrzej J.
6 Manafian Heris, Jalil
6 Mañosa, Víctor
6 Marchesiello, Antonella
6 Roberts, John Anthony Gerard
6 Roy Chowdhury, Asesh
6 Seadawy, Aly R.
6 Sun, Jianqing
6 Suris, Yuri Borisovich
6 Zhang, Jilong
5 Adler, Vsevolod Eduardovich
5 Chen, Yang
5 Halburd, Rodney G.
5 Hlavatý, Ladislav
5 Ishizaki, Katsuya
5 Kamiya, Ryo
5 Liu, Yinping
...and 1,457 more Authors
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Cited in 249 Serials

219 Journal of Mathematical Physics
124 Physics Letters. A
71 Chaos, Solitons and Fractals
70 Journal of Physics A: Mathematical and Theoretical
67 Physica D
64 Journal of Nonlinear Mathematical Physics
48 Applied Mathematics and Computation
31 Theoretical and Mathematical Physics
31 Studies in Applied Mathematics
30 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
28 Journal of Mathematical Analysis and Applications
24 Letters in Mathematical Physics
22 Computers & Mathematics with Applications
22 Physica A
21 Journal of Difference Equations and Applications
20 Communications in Nonlinear Science and Numerical Simulation
17 Applied Mathematics Letters
15 Journal of Geometry and Physics
15 Regular and Chaotic Dynamics
14 Communications in Mathematical Physics
14 Advances in Difference Equations
13 Journal of Differential Equations
11 Nonlinearity
11 Mathematics and Computers in Simulation
11 Acta Applicandae Mathematicae
10 Computer Physics Communications
10 Mathematical Methods in the Applied Sciences
10 Nonlinear Dynamics
9 International Journal of Theoretical Physics
9 Reports on Mathematical Physics
9 Proceedings of the American Mathematical Society
8 Nuclear Physics. B
8 Journal of Computational and Applied Mathematics
8 International Journal of Nonlinear Sciences and Numerical Simulation
7 International Journal of Modern Physics B
6 Modern Physics Letters A
6 Numerical Algorithms
6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
6 Chaos
6 Journal of High Energy Physics
6 Qualitative Theory of Dynamical Systems
6 International Journal of Geometric Methods in Modern Physics
6 Communications in Theoretical Physics
5 Reviews in Mathematical Physics
5 Journal of Approximation Theory
5 Mathematical and Computer Modelling
5 Japan Journal of Industrial and Applied Mathematics
5 International Journal of Computer Mathematics
5 Celestial Mechanics and Dynamical Astronomy
5 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
5 Physical Review Letters
5 Differential Equations
5 Advances in Mathematical Physics
5 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
4 International Journal of Modern Physics A
4 Applicable Analysis
4 Bulletin of the Australian Mathematical Society
4 International Journal of Engineering Science
4 Indian Journal of Pure & Applied Mathematics
4 Mathematical Notes
4 Wave Motion
4 ZAMP. Zeitschrift für angewandte Mathematik und Physik
4 Quaestiones Mathematicae
4 Constructive Approximation
4 Journal of Nonlinear Science
4 Bulletin des Sciences Mathématiques
4 Complexity
4 Abstract and Applied Analysis
4 Acta Mathematica Sinica. English Series
4 Nonlinear Analysis. Real World Applications
4 Computational Methods and Function Theory
4 Frontiers of Mathematics in China
4 Analysis and Mathematical Physics
4 East Asian Journal on Applied Mathematics
3 Journal of Fluid Mechanics
3 Physics Letters. B
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 Applied Numerical Mathematics
3 European Journal of Applied Mathematics
3 Annals of Physics
3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Journal of Algebraic Combinatorics
3 Journal of Mathematical Sciences (New York)
3 Mathematical Problems in Engineering
3 Mathematical Physics, Analysis and Geometry
3 Annales Henri Poincaré
3 The ANZIAM Journal
3 Dynamical Systems
3 Discrete and Continuous Dynamical Systems. Series B
3 Acta Mathematica Scientia. Series B. (English Edition)
3 Science China. Mathematics
3 Ufimskiĭ Matematicheskiĭ Zhurnal
3 Symmetry
3 Journal of Computational Dynamics
3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
...and 149 more Serials
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Cited in 54 Fields

752 Dynamical systems and ergodic theory (37-XX)
616 Partial differential equations (35-XX)
401 Ordinary differential equations (34-XX)
331 Difference and functional equations (39-XX)
139 Mechanics of particles and systems (70-XX)
110 Special functions (33-XX)
109 Quantum theory (81-XX)
85 Numerical analysis (65-XX)
75 Fluid mechanics (76-XX)
59 Algebraic geometry (14-XX)
55 Biology and other natural sciences (92-XX)
44 Functions of a complex variable (30-XX)
43 Global analysis, analysis on manifolds (58-XX)
41 Statistical mechanics, structure of matter (82-XX)
37 Computer science (68-XX)
36 Relativity and gravitational theory (83-XX)
35 Differential geometry (53-XX)
33 Nonassociative rings and algebras (17-XX)
20 Optics, electromagnetic theory (78-XX)
19 Harmonic analysis on Euclidean spaces (42-XX)
16 Linear and multilinear algebra; matrix theory (15-XX)
16 Topological groups, Lie groups (22-XX)
14 Number theory (11-XX)
13 Approximations and expansions (41-XX)
12 Systems theory; control (93-XX)
11 Integral equations (45-XX)
10 Commutative algebra (13-XX)
9 Field theory and polynomials (12-XX)
9 Associative rings and algebras (16-XX)
8 Combinatorics (05-XX)
8 Operator theory (47-XX)
8 Geometry (51-XX)
8 Information and communication theory, circuits (94-XX)
7 Several complex variables and analytic spaces (32-XX)
7 Mechanics of deformable solids (74-XX)
5 Probability theory and stochastic processes (60-XX)
4 Functional analysis (46-XX)
3 General and overarching topics; collections (00-XX)
3 Convex and discrete geometry (52-XX)
2 History and biography (01-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Group theory and generalizations (20-XX)
2 Real functions (26-XX)
2 Measure and integration (28-XX)
2 Abstract harmonic analysis (43-XX)
2 Geophysics (86-XX)
1 Potential theory (31-XX)
1 Sequences, series, summability (40-XX)
1 Integral transforms, operational calculus (44-XX)
1 General topology (54-XX)
1 Manifolds and cell complexes (57-XX)
1 Statistics (62-XX)
1 Astronomy and astrophysics (85-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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