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Winternitz, Pavel

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Author ID: winternitz.pavel Recent zbMATH articles by "Winternitz, Pavel"
Published as: Winternitz, P.; Winternitz, Pavel
Homepage: http://www.crm.umontreal.ca/~wintern/
External Links: MGP · Math-Net.Ru · Wikidata · ORCID · GND
Documents Indexed: 275 Publications since 1970, including 13 Books
Biographic References: 1 Publication
all top 5

Co-Authors

23 single-authored
43 Levi, Decio
28 Patera, Jiří
19 Harnad, John
19 Zassenhaus, Hans Julius
10 Sharp, Robert T.
9 Dorodnitsyn, Vladimir A.
9 Gagnon, Laurence S.
9 Hussin, Véronique
9 Martina, Luigi
9 Pogosyan, George S.
9 Thomova, Zora
7 del Olmo, Mariano A.
7 Grundland, Alfred Michel
7 Kalnins, Ernest G.
7 Lafortune, Stéphane
7 Rodriguez, Miguel Angel Rodriguez
6 Anderson, Robert Leonard
6 Grammaticos, Basil
6 Kozlov, Roman
6 Miller, Willard jun.
6 Post, Sarah
6 Ramani, Alfred
6 Sissakian, Aleksey N.
6 Šnobl, Libor
6 Tempesta, Piergiulio
6 Yurduşen, Ismet
5 Izmest’ev, A. A.
5 Marquette, Ian
5 Tremblay, Sébastien
4 Escobar-Ruiz, Mauricio A.
4 Heredero, R. Hernández
4 Turbiner, Alexander
4 Vinet, Luc
3 Beckers, J. V. L.
3 Boyer, Charles P.
3 Lopez Vieyra, Juan Carlos
3 Moshinsky, Marcos
3 Olver, Peter John
3 Rand, D. W.
3 Rebelo, Raphaël
3 Rideau, Guy
3 Rogers, Colin
3 Sheftel, Mikhail B.
3 Tremblay, Frédérick
2 Beckers, Joris
2 Bountis, Tassos C.
2 Bourlioux, Anne
2 Burdet, Guy
2 Champagne, Benoît
2 Clarkson, Peter A.
2 David, Damien
2 Dorizzi, Bernadette
2 Gómez-Ullate, David
2 Güngör, Faruk
2 Havlíček, Miloslav
2 Hernández Heredero, Rafael
2 Kaptsov, E. I.
2 Kibler, Maurice R.
2 Kozlov, R. V.
2 Kress, Jonathan M.
2 Marchesiello, Antonella
2 Meleshko, Sergey V.
2 Ndogmo, Jean-Claude
2 Orlov, Aleksandr Yu.
2 Papageorgiou, Vassilios G.
2 Perrin, Martine
2 Perroud, Marcel
2 Pošta, Severin
2 Raczka, Ryszard
2 Rashid, Muneer Ahmad
2 Rodríguez, Marco A.
2 Shnider, Steven
2 Smirnov, Roman G.
2 Yamilov, Ravil Islamovich
2 Zakrzewski, Wojciech J.
1 Abouamal, Ismail
1 Ait Abdelmalek, M.
1 Akhmediev, Nail N.
1 Ankiewicz, Adrian
1 Atakishiev, Natig M.
1 Ayari, M. Ali
1 Beckers, Jean-Marie
1 Beckers, Jules
1 Belinfante, Johan Gijsbertus Frederik
1 Berest, Yuri Yu.
1 Bérubé, Josée
1 Bihlo, Alexander
1 Bover, C. P.
1 Campoamor-Stursberg, Rutwig
1 Cariñena, José F.
1 Chacón, Edixon
1 Charest, François
1 Coiteux-Roy, Xavier
1 Coley, Alan Albert
1 Couture, Mathieu
1 Cyr-Gagnon, C.
1 Daboul, Jamil
1 Dattoli, Giuseppe
1 David, Dongo
1 Désilets, Jean-Francois
...and 45 more Co-Authors

Publications by Year

Citations contained in zbMATH Open

234 Publications have been cited 2,939 times in 1,571 Documents Cited by Year
Invariants of real low dimension Lie algebras. Zbl 0357.17004
Patera, J.; Sharp, R. T.; Winternitz, P.; Zassenhaus, Hans
156
1976
Subalgebras of real three- and four-dimensional Lie algebras. Zbl 0412.17007
Patera, J.; Winternitz, P.
98
1977
Non-classical symmetry reduction: Example of the Boussinesq equation. Zbl 0694.35159
Levi, D.; Winternitz, P.
97
1989
Classical and quantum superintegrability with applications. Zbl 1276.81070
Miller, Willard jun.; Post, Sarah; Winternitz, Pavel
75
2013
Continuous subgroups of the fundamental groups of physics. I: General method and the Poincaré group. Zbl 0314.22007
Patera, J.; Winternitz, P.; Zassenhaus, Hans
62
1975
Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable? Zbl 0619.35086
Dorizzi, B.; Grammaticos, B.; Ramani, A.; Winternitz, P.
57
1986
Symmetry reduction for the Kadomtsev-Petviashvili equation using a loop algebra. Zbl 0598.35117
David, D.; Kamran, N.; Levi, D.; Winternitz, P.
49
1986
Superintegrability with third-order integrals in quantum and classical mechanics. Zbl 1060.81034
Gravel, Simon; Winternitz, Pavel
45
2002
The computer calculation of Lie point symmetries of large systems of differential equations. Zbl 0875.65079
Champagne, B.; Hereman, W.; Winternitz, P.
45
1991
Normal forms of elements of classical real and complex Lie and Jordan algebras. Zbl 0544.17013
Đoković, Dragomir Ž.; Patera, J.; Winternitz, P.; Zassenhaus, Hans
41
1983
Exact solvability of superintegrable systems. Zbl 1011.81019
Tempesta, Piergiulio; Turbiner, Alexander V.; Winternitz, Pavel
39
2001
An infinite family of solvable and integrable quantum systems on a plane. Zbl 1166.81366
Tremblay, Frédérick; Turbiner, Alexander V.; Winternitz, Pavel
37
2009
Superintegrable systems in Darboux spaces. Zbl 1063.37050
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.; Winternitz, P.
34
2003
Symmetries of variable coefficient Korteweg-de Vries equations. Zbl 0767.35077
Gazeau, J. P.; Winternitz, P.
33
1992
Superintegrability in a two-dimensional space of nonconstant curvature. Zbl 1059.37040
Kalnins, E. G.; Kress, J. M.; Winternitz, P.
32
2002
Dynamical invariance algebra of the Hartmann potential. Zbl 0684.35083
Kibler, M.; Winternitz, P.
32
1987
Continuous subgroups of the fundamental groups of physics. III: The de Sitter groups. Zbl 0372.22008
Patera, J.; Sharp, R. T.; Winternitz, P.; Zassenhaus, Hans
32
1977
Classification and identification of Lie algebras. Zbl 1331.17001
Šnobl, Libor; Winternitz, Pavel
31
2014
Lie symmetries of a generalised nonlinear Schrödinger equation. II: Exact solutions. Zbl 0707.35145
Gagnon, L.; Winternitz, P.
31
1989
On the infinite-dimensional symmetry group of the Davey-Stewartson equations. Zbl 0643.35097
Champagne, B.; Winternitz, P.
31
1988
Superposition principles for matrix Riccati equations. Zbl 0556.34015
Harnad, J.; Winternitz, P.; Anderson, R. L.
31
1983
Symmetry classes of variable coefficient nonlinear Schrödinger equations. Zbl 0821.35128
Gagnon, L.; Winternitz, P.
30
1993
Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation. Zbl 0734.35123
Clarkson, P. A.; Winternitz, P.
30
1991
Integrable Hamiltonian systems with velocity-dependent potentials. Zbl 0586.70013
Dorizzi, B.; Grammaticos, B.; Ramani, A.; Winternitz, P.
29
1985
A new basis for the representations of the rotation group. Lame and Heun polynomials. Zbl 0285.22017
Patera, J.; Winternitz, P.
29
1973
Continuous symmetries of difference equations. Zbl 1112.37053
Levi, Decio; Winternitz, Pavel
28
2006
A class of solvable Lie algebras and their Casimir invariants. Zbl 1063.22023
Šnobl, L.; Winternitz, P.
27
2005
Lie symmetries of a generalised nonlinear Schrödinger equation. I: The symmetry group and its subgroups. Zbl 0694.35174
Gagnon, L.; Winternitz, P.
27
1988
The group O(4), separation of variables and the hydrogen atom. Zbl 0335.35002
Kalnins, E. G.; Miller, W. jun.; Winternitz, P.
27
1976
Lie group formalism for difference equations. Zbl 0956.39013
Levi, D.; Vinet, L.; Winternitz, P.
26
1997
Solvable Lie algebras with Abelian nilradicals. Zbl 0828.17009
Ndogmo, J. C.; Winternitz, P.
26
1994
Group theoretical analysis of dispersive long wave equations in two space dimensions. Zbl 0725.35104
Paquin, G.; Winternitz, P.
26
1990
Subgroups of the Poincaré group and their invariants. Zbl 0347.20029
Patera, J.; Sharp, R. T.; Winternitz, P.; Zassenhaus, Hans
25
1976
On the identification of a Lie algebra given by its structure constants. I: Direct decompositions, Levi decompositions, and nilradicals. Zbl 0668.17004
Rand, D. W.; Winternitz, P.; Zassenhaus, Hans
23
1988
Symmetry reduction for nonlinear relativistically invariant equations. Zbl 0599.70026
Grundland, A. M.; Harnad, J.; Winternitz, P.
23
1984
Lie group classification of second-order ordinary difference equations. Zbl 0981.39010
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel
22
2000
Symmetries of discrete dynamical systems. Zbl 0862.34049
Levi, D.; Winternitz, P.
22
1996
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
On the integrability of systems of nonlinear ordinary differential equations with superposition principles. Zbl 0589.34040
Bountis, T. C.; Papageorgiou, V.; Winternitz, P.
22
1986
Systems of ordinary differential equations with nonlinear superposition principles. Zbl 1194.34013
Anderson, R. L.; Harnad, J.; Winternitz, P.
22
1982
Complete sets of commuting operators and 0(3) scalars in the enveloping algebra of SU(3). Zbl 0289.22019
Judd, B. R.; Miller, W. jun.; Patera, J.; Winternitz, P.
22
1974
Integrable and superintegrable Hamiltonian systems in magnetic fields. Zbl 1052.37048
McSween, Eric; Winternitz, Pavel
21
2000
Symmetries and conditional symmetries of differential-difference equations. Zbl 0780.34047
Levi, D.; Winternitz, P.
21
1993
Classification of systems of nonlinear ordinary differential equations with superposition principles. Zbl 0586.34010
Shnider, S.; Winternitz, P.
21
1984
Periodic orbits for an infinite family of classical superintegrable systems. Zbl 1186.37069
Tremblay, Frédérick; Turbiner, Alexander V.; Winternitz, Pavel
20
2010
Solvable Lie algebras with triangular nilradicals. Zbl 1001.17011
Tremblay, S.; Winternitz, P.
20
1998
Lie groups and solutions of nonlinear partial differential equations. Zbl 0830.35004
Winternitz, P.
20
1993
Superposition laws for solutions of differential matrix Riccati equations arising in control theory. Zbl 0597.93023
Sorine, Michel; Winternitz, Pavel
20
1985
Polynomial irreducible tensors for point groups. Zbl 0464.20011
Patera, J.; Sharp, R. T.; Winternitz, P.
20
1978
Superintegrable systems with third-order integrals of motion. Zbl 1192.81189
Marquette, Ian; Winternitz, Pavel
18
2008
Quantum superintegrability and exact solvability in \(n\) dimensions. Zbl 1059.81081
Rodriguez, Miguel A.; Winternitz, Pavel
18
2002
Classical and quantum integrable systems in \(\widetilde{\mathfrak gl}(2)^{+*}\) and separation of variables. Zbl 0842.58046
Harnad, J.; Winternitz, P.
18
1995
Solvable Lie algebras with Heisenberg ideals. Zbl 0773.17004
Rubin, J. L.; Winternitz, P.
18
1993
Symmetry breaking interactions for the time dependent Schrödinger equation. Zbl 0326.35019
Boyer, C. P.; Sharp, R. T.; Winternitz, P.
18
1976
Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra. Zbl 1012.35074
Güngör, F.; Winternitz, P.
17
2002
Superintegrable systems in quantum mechanics and classical Lie theory. Zbl 1013.81020
Sheftel, M. B.; Tempesta, P.; Winternitz, P.
17
2001
The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1). Zbl 0291.20059
Patera, J.; Winternitz, P.; Zassenhaus, Hans
17
1974
Integrable and superintegrable quantum systems in a magnetic field. Zbl 1071.81037
Bérubé, Josée; Winternitz, Pavel
16
2004
Group theoretical approach to superposition rules for systems of Riccati equations. Zbl 0474.34011
Anderson, R. L.; Harnad, J.; Winternitz, P.
16
1981
Tensor fields invariant under subgroups of the conformal group of space- time. Zbl 0419.53013
Beckers, J.; Harnad, J.; Perroud, M.; Winternitz, P.
16
1978
Polynomial Poisson algebras for classical superintegrable systems with a third-order integral of motion. Zbl 1121.37043
Marquette, Ian; Winternitz, Pavel
14
2007
Analysis and applications of the symmetry group of the multidimensional three-wave resonant interaction problem. Zbl 0875.58029
Martina, L.; Winternitz, P.
14
1989
Integrable nonlinear equations for water waves in straits of varying depth and width. Zbl 0678.35008
David, D.; Levi, D.; Winternitz, P.
14
1987
Abelian integrals and the reduction method for an integrable Hamiltonian system. Zbl 0597.70020
Gagnon, L.; Harnad, J.; Winternitz, P.; Hurtubise, J.
14
1985
Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics. Zbl 0342.22015
Beckers, J.; Patera, J.; Perroud, M.; Winternitz, P.
14
1977
Higher indices for group representations. Zbl 0347.22010
Patera, J.; Sharp, R. T.; Winternitz, P.
14
1976
Continuous subgroups of the fundamental groups of physics. II: The similitude group. Zbl 0314.22008
Patera, J.; Winternitz, P.; Zassenhaus, Hans
14
1975
The maximal solvable subgroups of SO(p,q) groups. Zbl 0339.22019
Patera, J.; Winternitz, P.; Zassenhaus, Hans
14
1974
Umbral calculus, difference equations and the discrete Schrödinger equation. Zbl 1064.39020
Levi, Decio; Tempesta, Piergiulio; Winternitz, Pavel
13
2004
Continuous symmetries of Lagrangians and exact solutions of discrete equations. Zbl 1070.70010
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel
13
2004
Lie-theoretical generalization and discretization of the Pinney equation. Zbl 0910.34013
Rogers, C.; Schief, W. K.; Winternitz, P.
13
1997
Everything you always wanted to know about \(SU(3)\subset 0(3)\). Zbl 0319.22017
Moshinsky, M.; Patera, J.; Sharp, R. T.; Winternitz, P.
13
1975
An infinite family of superintegrable deformations of the Coulomb potential. Zbl 1190.81043
Post, Sarah; Winternitz, Pavel
12
2010
Group foliation and non-invariant solutions of the heavenly equation. Zbl 1002.35010
Martina, L.; Sheftel, M. B.; Winternitz, P.
12
2001
Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras. Zbl 0546.34008
Shnider, S.; Winternitz, P.
12
1984
Lie groups and solutions of nonlinear differential equations. Zbl 0571.34002
Winternitz, Pavel
12
1983
Maximal Abelian subalgebras of real and complex symplectic Lie algebras. Zbl 0559.17005
Patera, J.; Winternitz, P.; Zassenhaus, Hans
12
1983
Subgroups of Lie groups and separation of variables. Zbl 0476.58021
Miller, W. jun.; Patera, J.; Winternitz, P.
12
1981
Third-order superintegrable systems separating in polar coordinates. Zbl 1188.81108
Tremblay, Frédérick; Winternitz, Pavel
11
2010
Difference schemes with point symmetries and their numerical tests. Zbl 1095.65070
Bourlioux, A.; Cyr-Gagnon, C.; Winternitz, P.
11
2006
Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations. Zbl 0956.65081
Dorodnitsyn, V.; Winternitz, P.
11
2000
Symmetries of the discrete Burgers equation. Zbl 0941.35093
Hernández Heredero, R.; Levi, D.; Winternitz, P.
11
1999
Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev-Petviashvili hierarchy. Zbl 0887.58024
Orlov, A. Yu.; Winternitz, P.
11
1997
Maximal abelian subalgebras of pseudounitary Lie algebras. Zbl 0723.17005
del Olmo, Mariano A.; Rodríguez, M. A.; Winternitz, P.; Zassenhaus, Hans
11
1990
Solitons in shallow seas of variable depth and in marine straits. Zbl 0728.76023
David, D.; Levi, D.; Winternitz, P.
11
1989
Separation of variables for the Hamilton-Jacobi equation on complex projective spaces. Zbl 0569.35012
Boyer, C. P.; Kalnins, E. G.; Winternitz, P.
11
1985
Lie point symmetries of difference equations and lattices. Zbl 0966.39007
Levi, D.; Tremblay, S.; Winternitz, P.
10
2000
Lie algebra contractions and symmetries of the Toda hierarchy. Zbl 0973.37046
Hernández Heredero, R.; Levi, D.; Rodríguez, M. A.; Winternitz, P.
10
2000
On the relation between weak and strong invariance of differential equations. Zbl 0826.58043
Cariñena, José F.; del Olmo, M. A.; Winternitz, P.
10
1993
Evolution equations invariant under two-dimensional space-time Schrödinger group. Zbl 0774.35066
Rideau, G.; Winternitz, P.
10
1993
Superposition formulas for rectangular matrix Riccati equations. Zbl 0628.34010
del Olmo, Mariano A.; Rodríguez, M. A.; Winternitz, P.
10
1987
The optical group and its subgroups. Zbl 0382.22010
Burdet, G.; Patera, J.; Perrin, M.; Winternitz, P.
10
1978
Subgroups of the similitude group of three-dimensional Minkowski space. Zbl 0982.81513
Patera, J.; Winternitz, P.; Sharp, R. T.; Zassenhaus, H.
10
1976
Clebsch-Gordan coefficients for the coupling of \(SL(2,C)\) principal- series representations. Zbl 0192.48502
Anderson, R. L.; Raczka, R.; Rashid, M. A.; Winternitz, P.
10
1970
General \(N\)th order integrals of motion in the Euclidean plane. Zbl 1327.81225
Post, S.; Winternitz, P.
9
2015
Integrable and superintegrable systems with spin in three-dimensional Euclidean space. Zbl 1178.81112
Winternitz, Pavel; Yurduşen, İsmet
9
2009
Heisenberg algebra, umbral calculus and orthogonal polynomials. Zbl 1152.81396
Dattoli, G.; Levi, D.; Winternitz, P.
9
2008
Grading refinements in the contractions of Lie algebras and their invariants. Zbl 0905.17036
Ait Abdelmalek, M.; Leng, X.; Patera, J.; Winternitz, P.
9
1996
Contractions of Lie algebras and separation of variables. Zbl 0901.17002
Izmest’ev, A. A.; Pogosyan, G. S.; Sissakian, A. N.; Winternitz, P.
9
1996
Integrable systems based on \(\text{SU}(p,q)\) homogeneous manifolds. Zbl 0783.58034
Del Olmo, Mariano A.; Rodríguez, M. A.; Winternitz, P.
9
1993
Corrigendum: Fourth order superintegrable systems separating in polar coordinates. I: Exotic potentials (J. Phys. A: Math. Theor. 50 495206)). Zbl 1422.35139
Escobar-Ruiz, Adrian M.; López Vieyra, J. C.; Winternitz, P.
1
2019
Fifth-order superintegrable quantum systems separating in Cartesian coordinates: doubly exotic potentials. Zbl 1385.81027
Abouamal, Ismail; Winternitz, Pavel
5
2018
Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries. Zbl 1402.34070
Dorodnitsyn, Vladimir A; Kozlov, Roman; Meleshko, Sergey V; Winternitz, Pavel
3
2018
Lie group classification of first-order delay ordinary differential equations. Zbl 1397.34106
Dorodnitsyn, Vladimir A; Kozlov, Roman; Meleshko, Sergey V; Winternitz, Pavel
3
2018
Spherical type integrable classical systems in a magnetic field. Zbl 1391.70051
Marchesiello, A.; Šnobl, L.; Winternitz, P.
3
2018
General \(N\)th-order superintegrable systems separating in polar coordinates. Zbl 1407.70024
Escobar-Ruiz, A. M.; Winternitz, P.; Yurduşen, İ
2
2018
Lie point symmetries and ODEs passing the Painlevé test. Zbl 1417.34211
Levi, D.; Sekera, D.; Winternitz, P.
2
2018
Fourth-order superintegrable systems separating in polar coordinates. II: Standard potentials. Zbl 1410.35153
Escobar-Ruiz, Adrian M.; Vieyra, J. C. López; Winternitz, P.; Yurduşen, İ
1
2018
Conformally invariant elliptic Liouville equation and its symmetry-preserving discretization. Zbl 1409.35087
Levi, D.; Martina, L.; Winternitz, P.
1
2018
Fourth order superintegrable systems separating in Cartesian coordinates. I: Exotic quantum potentials. Zbl 1447.70019
Marquette, Ian; Sajedi, Masoumeh; Winternitz, Pavel
7
2017
Fourth order superintegrable systems separating in polar coordinates. I: Exotic potentials. Zbl 1394.35385
Escobar-Ruiz, A. M.; López Vieyra, J. C.; Winternitz, P.
6
2017
Symmetry preserving discretization of ordinary differential equations. large symmetry groups and higher order equations. Zbl 1344.65069
Campoamor-Stursberg, R.; Rodríguez, M. A.; Winternitz, P.
2
2016
General \(N\)th order integrals of motion in the Euclidean plane. Zbl 1327.81225
Post, S.; Winternitz, P.
9
2015
Three-dimensional superintegrable systems in a static electromagnetic field. Zbl 1397.81096
Marchesiello, A.; Šnobl, L.; Winternitz, P.
8
2015
Structure preserving discretizations of the Liouville equation and their numerical tests. Zbl 1358.35072
Levi, Decio; Martina, Luigi; Winternitz, Pavel
6
2015
Lie-point symmetries of the discrete Liouville equation. Zbl 1315.37042
Levi, D.; Martina, L.; Winternitz, P.
5
2015
The adjoint equation method for constructing first integrals of difference equations. Zbl 1315.39001
Dorodnitsyn, V.; Kaptsov, E.; Kozlov, R.; Winternitz, P.
4
2015
The Korteweg-de Vries equation and its symmetry-preserving discretization. Zbl 1319.35214
Bihlo, Alexander; Coiteux-Roy, Xavier; Winternitz, Pavel
3
2015
Classification and identification of Lie algebras. Zbl 1331.17001
Šnobl, Libor; Winternitz, Pavel
31
2014
Superintegrable systems with spin induced by co-algebra symmetry. Zbl 1286.81108
Riglioni, D.; Gingras, O.; Winternitz, P.
2
2014
Lie group analysis of a generalized Krichever-Novikov differential-difference equation. Zbl 1366.39015
Levi, Decio; Ricca, Eugenio; Thomova, Zora; Winternitz, Pavel
1
2014
First integrals of difference equations which do not possess a variational formulation. Zbl 1297.39011
Winternitz, P.; Dorodnitsyn, V. A.; Kaptsov, E. I.; Kozlov, R. V.
1
2014
Classical and quantum superintegrability with applications. Zbl 1276.81070
Miller, Willard jun.; Post, Sarah; Winternitz, Pavel
75
2013
Superintegrable systems with spin and second-order integrals of motion. Zbl 1258.81027
Désilets, Jean-Francois; Winternitz, Pavel; Yurduşen, İsmet
6
2012
Third-order superintegrable systems separable in parabolic coordinates. Zbl 1277.70020
Popper, I.; Post, S.; Winternitz, P.
5
2012
Infinite families of superintegrable systems separable in subgroup coordinates. Zbl 1348.70047
Lévesque, Daniel; Post, Sarah; Winternitz, Pavel
2
2012
Solvable Lie algebras with Borel nilradicals. Zbl 1302.17020
Šnobl, L.; Winternitz, P.
1
2012
Contact transformations for difference schemes. Zbl 1239.65054
Levi, Decio; Scimiterna, Christian; Thomova, Zora; Winternitz, Pavel
1
2012
A nonseparable quantum superintegrable system in 2D real Euclidean space. Zbl 1214.81107
Post, Sarah; Winternitz, Pavel
8
2011
Symmetries of the continuous and discrete Krichever-Novikov equation. Zbl 1244.35004
Levi, Decio; Winternitz, Pavel; Yamilov, Ravil I.
5
2011
Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations. Zbl 1229.65133
Winternitz, Pavel
4
2011
Are there contact transformations for discrete equations? Zbl 1227.39002
Levi, Decio; Thomova, Zora; Winternitz, Pavel
1
2011
Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Zbl 1218.39002
Levi, Decio (ed.); Olver, Peter (ed.); Thomova, Zora (ed.); Winternitz, Pavel (ed.)
1
2011
Periodic orbits for an infinite family of classical superintegrable systems. Zbl 1186.37069
Tremblay, Frédérick; Turbiner, Alexander V.; Winternitz, Pavel
20
2010
An infinite family of superintegrable deformations of the Coulomb potential. Zbl 1190.81043
Post, Sarah; Winternitz, Pavel
12
2010
Third-order superintegrable systems separating in polar coordinates. Zbl 1188.81108
Tremblay, Frédérick; Winternitz, Pavel
11
2010
Lie point symmetries of differential-difference equations. Zbl 1197.35303
Levi, D.; Winternitz, P.; Yamilov, R. I.
6
2010
An infinite family of solvable and integrable quantum systems on a plane. Zbl 1166.81366
Tremblay, Frédérick; Turbiner, Alexander V.; Winternitz, Pavel
37
2009
Integrable and superintegrable systems with spin in three-dimensional Euclidean space. Zbl 1178.81112
Winternitz, Pavel; Yurduşen, İsmet
9
2009
All solvable extensions of a class of nilpotent Lie algebras of dimension \(n\) and degree of nilpotency \(n-1\). Zbl 1178.17009
Šnobl, L.; Winternitz, P.
4
2009
Invariant difference schemes and their application to \(sl(2, \mathbb {R})\) invariant ordinary differential equations. Zbl 1178.65080
Rebelo, R.; Winternitz, P.
3
2009
Groups and symmetries. From Neolithic Scots to John McKay. Selected papers of the conference, Montreal, Canada, April 27–29, 2007. Zbl 1167.20300
Harnad, John (ed.); Winternitz, Pavel (ed.)
1
2009
Superintegrable systems with third-order integrals of motion. Zbl 1192.81189
Marquette, Ian; Winternitz, Pavel
18
2008
Heisenberg algebra, umbral calculus and orthogonal polynomials. Zbl 1152.81396
Dattoli, G.; Levi, D.; Winternitz, P.
9
2008
Symmetry preserving discretization of SL\((2,\mathbb{R})\) invariant equations. Zbl 1362.65076
Bourlioux, Anne; Rebelo, Raphaël; Winternitz, Pavel
5
2008
Erratum: Polynomial Poisson algebras for classical superintegrable systems with a third order integral of motion. Zbl 1153.37402
Marquette, I.; Winternitz, P.
2
2008
Polynomial Poisson algebras for classical superintegrable systems with a third-order integral of motion. Zbl 1121.37043
Marquette, Ian; Winternitz, Pavel
14
2007
Quasiseparation of variables in the Schrödinger equation with a magnetic field. Zbl 1121.81064
Charest, F.; Hudon, C.; Winternitz, P.
5
2007
Erratum: ”A class of superintegrable systems of Calogero type”. Zbl 1144.81414
Smirnov, Roman G.; Winternitz, Pavel
2
2007
Continuous symmetries of difference equations. Zbl 1112.37053
Levi, Decio; Winternitz, Pavel
28
2006
Difference schemes with point symmetries and their numerical tests. Zbl 1095.65070
Bourlioux, A.; Cyr-Gagnon, C.; Winternitz, P.
11
2006
Integrable and superintegrable systems with spin. Zbl 1112.70016
Winternitz, Pavel; Yurduşen, İsmet
8
2006
A class of superintegrable systems of Calogero type. Zbl 1112.81052
Smirnov, Roman G.; Winternitz, Pavel
6
2006
A class of solvable Lie algebras and their Casimir invariants. Zbl 1063.22023
Šnobl, L.; Winternitz, P.
27
2005
Discretization of partial differential equations preserving their physical symmetries. Zbl 1078.76051
Valiquette, F.; Winternitz, P.
7
2005
Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schrödinger equations. Zbl 1080.35105
Kalnins, E. G.; Thomova, Z.; Winternitz, P.
2
2005
Integrable and superintegrable quantum systems in a magnetic field. Zbl 1071.81037
Bérubé, Josée; Winternitz, Pavel
16
2004
Umbral calculus, difference equations and the discrete Schrödinger equation. Zbl 1064.39020
Levi, Decio; Tempesta, Piergiulio; Winternitz, Pavel
13
2004
Continuous symmetries of Lagrangians and exact solutions of discrete equations. Zbl 1070.70010
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel
13
2004
Superintegrability in classical and quantum systems. Proceedings of a workshop, Montréal, Canada, September 16–21, 2002. Zbl 1055.37004
Tempesta, P. (ed.); Winternitz, P. (ed.); Harnad, J. (ed.); Miller, W. jun. (ed.); Pogosyan, G. (ed.); Rodriguez, M. (ed.)
8
2004
Equivalence classes and symmetries of the variable coefficient Kadomtsev-Petviashvili equation. Zbl 1059.35117
Güngör, F.; Winternitz, P.
6
2004
Lie symmetries and exact solutions of first-order difference schemes. Zbl 1070.65057
Rodríguez, M. A.; Winternitz, P.
4
2004
Superintegrable systems in classical and quantum mechanics. Zbl 1064.35156
Winternitz, P.
2
2004
Subalgebras of Lie algebras. Example of \(\text{sl} (3,\mathbb R)\). Zbl 1065.81069
Winternitz, Pavel
1
2004
Superintegrable systems in Darboux spaces. Zbl 1063.37050
Kalnins, E. G.; Kress, J. M.; Miller, W. jun.; Winternitz, P.
34
2003
Weak transversality and partially invariant solutions. Zbl 1062.35063
Grundland, A. M.; Tempesta, P.; Winternitz, P.
8
2003
Symmetries, Lagrangian formalism and integration of second order ordinary difference equations. Zbl 1362.39008
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel
4
2003
Superintegrability with third-order integrals in quantum and classical mechanics. Zbl 1060.81034
Gravel, Simon; Winternitz, Pavel
45
2002
Superintegrability in a two-dimensional space of nonconstant curvature. Zbl 1059.37040
Kalnins, E. G.; Kress, J. M.; Winternitz, P.
32
2002
Quantum superintegrability and exact solvability in \(n\) dimensions. Zbl 1059.81081
Rodriguez, Miguel A.; Winternitz, Pavel
18
2002
Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra. Zbl 1012.35074
Güngör, F.; Winternitz, P.
17
2002
Separation of variables and subgroup bases on \(n\)-dimensional hyperboloids. Zbl 1060.33022
Pogosyan, G. S.; Winternitz, P.
4
2002
Lie point symmetries and commuting flows for equations on lattices. Zbl 1215.39008
Levi, D.; Winternitz, P.
4
2002
Exact solvability of superintegrable systems. Zbl 1011.81019
Tempesta, Piergiulio; Turbiner, Alexander V.; Winternitz, Pavel
39
2001
Superintegrable systems in quantum mechanics and classical Lie theory. Zbl 1013.81020
Sheftel, M. B.; Tempesta, P.; Winternitz, P.
17
2001
Group foliation and non-invariant solutions of the heavenly equation. Zbl 1002.35010
Martina, L.; Sheftel, M. B.; Winternitz, P.
12
2001
Lie symmetries of multidimensional difference equations. Zbl 0998.39008
Levi, D.; Tremblay, S.; Winternitz, P.
7
2001
Contractions of Lie algebras and the separation of variables: interbase expansions. Zbl 1058.81031
Izmest’ev, A. A.; Pogosyan, G. S.; Sissakian, A. N.; Winternitz, P.
7
2001
Symmetry classification of diatomic molecular chains. Zbl 1018.81056
Lafortune, S.; Tremblay, S.; Winternitz, P.
5
2001
Invariants of the nilpotent and solvable triangular Lie algebras. Zbl 1001.17012
Tremblay, S.; Winternitz, P.
3
2001
Symmetries of the discrete nonlinear Schrödinger equation. Zbl 1002.39031
Hernández Heredero, R.; Levi, D.; Winternitz, P.
2
2001
Lie group classification of second-order ordinary difference equations. Zbl 0981.39010
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel
22
2000
Integrable and superintegrable Hamiltonian systems in magnetic fields. Zbl 1052.37048
McSween, Eric; Winternitz, Pavel
21
2000
Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations. Zbl 0956.65081
Dorodnitsyn, V.; Winternitz, P.
11
2000
Lie point symmetries of difference equations and lattices. Zbl 0966.39007
Levi, D.; Tremblay, S.; Winternitz, P.
10
2000
Lie algebra contractions and symmetries of the Toda hierarchy. Zbl 0973.37046
Hernández Heredero, R.; Levi, D.; Rodríguez, M. A.; Winternitz, P.
10
2000
Invariant solutions of hydrodynamic-type equations. Zbl 0961.35117
Grundland, A. M.; Sheftel, M. B.; Winternitz, P.
5
2000
Point symmetries of generalized Toda field theories. II: Symmetry reduction. Zbl 1064.37506
Martina, L.; Lafortune, S.; Winternitz, P.
3
2000
Symmetry preserving discretization of the Burgers equation. Zbl 0963.35168
Hernández Heredero, R.; Levi, D.; Winternitz, P.
2
2000
Integrable systems: from classical to quantum. Proceedings of the 38th session of the Séminaire de mathématiques supérieures, Montréal, Canada, July 26–August 6, 1999. Zbl 0952.00031
Harnad, J. (ed.); Sabidussi, G. (ed.); Winternitz, P. (ed.)
1
2000
Bases for representations of quantum algebras. Zbl 1041.17013
Atakishiyev, N. M.; Winternitz, P.
1
2000
On Lie group classification of second-order ordinary difference equations. Zbl 0959.39017
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel
1
2000
Point symmetries of generalized Toda field theories. Zbl 0971.81151
Lafortune, S.; Winternitz, P.; Martina, L.
1
2000
Symmetries of the discrete Burgers equation. Zbl 0941.35093
Hernández Heredero, R.; Levi, D.; Winternitz, P.
11
1999
Symmetries of discrete dynamical systems involving two species. Zbl 0977.37035
Gómez-Ullate, D.; Lafortune, S.; Winternitz, P.
7
1999
Contractions of Lie algebras and separation of variables. The \(n\)-dimensional sphere. Zbl 1055.17500
Izmest’ev, A. A.; Pogosyan, G. S.; Sissakian, A. N.; Winternitz, P.
7
1999
Symmetry reduction and exact solutions of nonlinear partial differential equations. Zbl 1032.35153
Clarkson, Peter A.; Winternitz, Pavel
5
1999
Group invariant solutions for the \(N=2\) super Korteweg-de Vries equation. Zbl 0946.35084
Ayari, M. A.; Hussin, V.; Winternitz, P.
5
1999
Nonlinear superposition formulas based on imprimitive group action. Zbl 0968.34006
Havlíček, M.; Pošta, S.; Winternitz, P.
3
1999
Graded contractions of the Lie algebra \(e(2,1)\). Zbl 1017.17028
Patera, J.; Pogosyan, G.; Winternitz, P.
3
1999
...and 134 more Documents
all top 5

Cited by 1,704 Authors

107 Winternitz, Pavel
36 Patera, Jiří
29 Kalnins, Ernest G.
26 Ma, Wen-Xiu
26 Miller, Willard jun.
26 Popovych, Roman O.
21 Cariñena, José F.
20 Grundland, Alfred Michel
19 Levi, Decio
19 Marquette, Ian
18 Clarkson, Peter A.
17 Vinet, Luc
16 de Lucas, Javier
15 Fushchych, Vil’gel’m Illich
15 Rañada, Manuel F.
15 Sharp, Robert T.
14 Hussin, Véronique
14 Leach, Peter Gavin Lawrence
14 Zassenhaus, Hans Julius
13 del Olmo, Mariano A.
13 Güngör, Faruk
13 Harnad, John
13 Pogosyan, George S.
13 Qu, Changzheng
13 Zhdanov, Renat Z.
12 Folly-Gbetoula, Mensah K.
12 Sophocleous, Christodoulos
11 Dorodnitsyn, Vladimir A.
11 Rogers, Colin
10 Gandarias Núñez, Maria Luz
10 Lou, Senyue
10 Nucci, Maria Clara
10 Omirov, Bakhrom A.
9 Bihlo, Alexander
9 Bruzón, Maria Santos
9 Campoamor-Stursberg, Rutwig
9 Escobar-Ruiz, Mauricio A.
9 Herranz, Francisco José
9 Mahomed, Fazal M.
9 Quesne, Christiane
9 Rezaei-Aghdam, Adel
9 Rodman, Leiba X.
9 Santander, Mariano
9 Thompson, Gerard
9 Tian, Bo
9 Zhang, Hongqing
8 Ballesteros, Angel
8 Barannyk, Leonid F.
8 Chen, Yong
8 Gaeta, Giuseppe
8 Huang, Dingjiang
8 Ivanova, Nataliya M.
8 Khudoyberdiyev, Abror Kh.
8 Kress, Jonathan M.
8 Lahno, Victor Ivanovich
8 Özemir, Cihangir
8 Rastelli, Giovanni
8 Sahadevan, Ramajayam
8 Vaneeva, Olena O.
8 Zhang, Jiefang
7 Azad, Hassan
7 Bluman, George W.
7 Borisov, Alekseĭ Vladimirovich
7 Boyer, Charles P.
7 Chanu, Claudia Maria
7 Dai, Chaoqing
7 Fordy, Allan P.
7 Ghanam, Ryad A.
7 Govinder, Keshlan Sathasiva
7 Grammaticos, Basil
7 Hariton, Alexander J.
7 Huang, Qing
7 Kozlov, Roman
7 Mamaev, Ivan Sergeevich
7 Meleshko, Sergey V.
7 Nikitin, Anatoly Glebovich
7 Nyirenda, Darlison
7 Ragnisco, Orlando
7 Ramani, Alfred
7 Sardón, Cristina
7 Sergyeyev, Artur
7 Šnobl, Libor
7 Tamizhmani, K. M.
7 Tempesta, Piergiulio
7 Tsyganov, Andreĭ Vladimirovich
7 Turbiner, Alexander
7 Valiquette, Francis
7 Wolf, Kurt Bernardo
6 Anderson, Ian M.
6 Bizyaev, Ivan Alekseevich
6 Błaszak, Maciej
6 Cherniha, Roman M.
6 Cicogna, Giampaolo
6 Conte, Robert M.
6 Dunajski, Maciej
6 Gao, Yitian
6 Genest, Vincent X.
6 Kara, Abdul Hamid
6 Kim, Dae San
6 Kim, Taekyun
...and 1,604 more Authors
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Cited in 223 Serials

448 Journal of Mathematical Physics
69 Journal of Mathematical Analysis and Applications
55 Linear Algebra and its Applications
43 Applied Mathematics and Computation
38 Journal of Nonlinear Mathematical Physics
30 Physics Letters. A
30 Journal of Geometry and Physics
26 Theoretical and Mathematical Physics
26 Acta Applicandae Mathematicae
26 Communications in Nonlinear Science and Numerical Simulation
26 Journal of Physics A: Mathematical and Theoretical
24 International Journal of Theoretical Physics
23 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
22 Computers & Mathematics with Applications
21 Chaos, Solitons and Fractals
20 Letters in Mathematical Physics
19 International Journal of Geometric Methods in Modern Physics
17 Communications in Mathematical Physics
17 Ukrainian Mathematical Journal
17 Nonlinear Dynamics
17 Journal of High Energy Physics
15 Regular and Chaotic Dynamics
14 Communications in Algebra
14 Physica D
13 Nuclear Physics. B
13 Studies in Applied Mathematics
11 International Journal of Modern Physics A
11 Advances in Mathematical Physics
10 Journal of Differential Equations
10 Annals of Physics
10 Symmetry
9 Journal of Algebra
9 Journal of Difference Equations and Applications
8 Computer Physics Communications
8 Reviews in Mathematical Physics
8 Differential Geometry and its Applications
8 Abstract and Applied Analysis
7 General Relativity and Gravitation
7 Journal of Engineering Mathematics
7 Reports on Mathematical Physics
7 Journal of Symbolic Computation
7 Applied Mathematics Letters
7 European Journal of Applied Mathematics
7 Journal of Mathematical Sciences (New York)
7 Journal of Mathematical Chemistry
6 Modern Physics Letters A
6 Linear and Multilinear Algebra
6 Mathematical Methods in the Applied Sciences
6 Mathematical and Computer Modelling
5 Journal of Pure and Applied Algebra
5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
5 Proceedings of the American Mathematical Society
5 Analysis and Mathematical Physics
4 International Journal of Modern Physics B
4 Journal of Computational Physics
4 Journal of Fluid Mechanics
4 Journal of Computational and Applied Mathematics
4 Journal of Soviet Mathematics
4 Quaestiones Mathematicae
4 Transactions of the American Mathematical Society
4 Annals of Global Analysis and Geometry
4 Celestial Mechanics and Dynamical Astronomy
4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
4 Advances in Difference Equations
4 Communications in Theoretical Physics
4 Mathematics
3 Journal of Statistical Physics
3 Physics Letters. B
3 Physics Reports
3 Mathematics of Computation
3 Results in Mathematics
3 Ricerche di Matematica
3 Applied Mathematics and Mechanics. (English Edition)
3 Discrete and Continuous Dynamical Systems
3 Chaos
3 International Journal of Modern Physics C
3 Frontiers of Mathematics in China
3 Advances in High Energy Physics
3 Journal of Nonlinear Science and Applications
3 Journal of Mathematics
3 International Journal of Applied and Computational Mathematics
2 Modern Physics Letters B
2 Acta Mechanica
2 Classical and Quantum Gravity
2 International Journal of Control
2 Physica A
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 BIT
2 Osaka Journal of Mathematics
2 Siberian Mathematical Journal
2 Applied Numerical Mathematics
2 Acta Mathematicae Applicatae Sinica. English Series
2 Forum Mathematicum
2 Computational and Applied Mathematics
2 Integral Transforms and Special Functions
2 Complexity
2 Transformation Groups
2 Journal of Inequalities and Applications
...and 123 more Serials
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Cited in 56 Fields

594 Partial differential equations (35-XX)
384 Dynamical systems and ergodic theory (37-XX)
344 Quantum theory (81-XX)
281 Nonassociative rings and algebras (17-XX)
181 Ordinary differential equations (34-XX)
180 Topological groups, Lie groups (22-XX)
177 Mechanics of particles and systems (70-XX)
137 Differential geometry (53-XX)
125 Global analysis, analysis on manifolds (58-XX)
96 Fluid mechanics (76-XX)
68 Special functions (33-XX)
68 Relativity and gravitational theory (83-XX)
58 Difference and functional equations (39-XX)
49 Numerical analysis (65-XX)
40 Linear and multilinear algebra; matrix theory (15-XX)
40 Computer science (68-XX)
36 Group theory and generalizations (20-XX)
25 Statistical mechanics, structure of matter (82-XX)
21 Operator theory (47-XX)
19 Algebraic geometry (14-XX)
19 Mechanics of deformable solids (74-XX)
18 Optics, electromagnetic theory (78-XX)
16 Number theory (11-XX)
15 Combinatorics (05-XX)
12 Functional analysis (46-XX)
12 Systems theory; control (93-XX)
11 Functions of a complex variable (30-XX)
11 Manifolds and cell complexes (57-XX)
11 Biology and other natural sciences (92-XX)
10 Commutative algebra (13-XX)
10 Associative rings and algebras (16-XX)
10 Calculus of variations and optimal control; optimization (49-XX)
9 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
8 Several complex variables and analytic spaces (32-XX)
8 Probability theory and stochastic processes (60-XX)
7 Geometry (51-XX)
6 Harmonic analysis on Euclidean spaces (42-XX)
4 Abstract harmonic analysis (43-XX)
3 Classical thermodynamics, heat transfer (80-XX)
3 Geophysics (86-XX)
2 Mathematical logic and foundations (03-XX)
2 Category theory; homological algebra (18-XX)
2 Real functions (26-XX)
2 Potential theory (31-XX)
2 Integral transforms, operational calculus (44-XX)
2 Integral equations (45-XX)
2 Algebraic topology (55-XX)
2 Statistics (62-XX)
2 Information and communication theory, circuits (94-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Field theory and polynomials (12-XX)
1 Sequences, series, summability (40-XX)
1 Approximations and expansions (41-XX)
1 General topology (54-XX)
1 Astronomy and astrophysics (85-XX)

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