Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel Second-order delay ordinary differential equations, their symmetries and application to a traffic problem. (English) Zbl 1519.34074 J. Phys. A, Math. Theor. 54, No. 10, Article ID 105204, 28 p. (2021). MSC: 34K05 22E05 34C14 76A30 90B20 PDFBibTeX XMLCite \textit{V. A. Dorodnitsyn} et al., J. Phys. A, Math. Theor. 54, No. 10, Article ID 105204, 28 p. (2021; Zbl 1519.34074) Full Text: DOI arXiv
Marquette, Ian; Sajedi, Masoumeh; Winternitz, Pavel Two-dimensional superintegrable systems from operator algebras in one dimension. (English) Zbl 1507.81117 J. Phys. A, Math. Theor. 52, No. 11, Article ID 115202, 27 p. (2019). MSC: 81R12 70H06 37J35 17B80 81Q05 81Q60 PDFBibTeX XMLCite \textit{I. Marquette} et al., J. Phys. A, Math. Theor. 52, No. 11, Article ID 115202, 27 p. (2019; Zbl 1507.81117) Full Text: DOI arXiv
Escobar-Ruiz, A. M.; Winternitz, P.; Yurduşen, İ General \(N\)th-order superintegrable systems separating in polar coordinates. (English) Zbl 1407.70024 J. Phys. A, Math. Theor. 51, No. 40, Article ID 40LT01, 12 p. (2018). MSC: 70H05 70H06 34M55 81Q10 81R12 PDFBibTeX XMLCite \textit{A. M. Escobar-Ruiz} et al., J. Phys. A, Math. Theor. 51, No. 40, Article ID 40LT01, 12 p. (2018; Zbl 1407.70024) Full Text: DOI arXiv
Abouamal, Ismail; Winternitz, Pavel Fifth-order superintegrable quantum systems separating in Cartesian coordinates: doubly exotic potentials. (English) Zbl 1385.81027 J. Math. Phys. 59, No. 2, 022104, 27 p. (2018). Reviewer: Willard Miller jun. (Minneapolis) MSC: 81R12 81Q10 81R05 33E17 34M55 PDFBibTeX XMLCite \textit{I. Abouamal} and \textit{P. Winternitz}, J. Math. Phys. 59, No. 2, 022104, 27 p. (2018; Zbl 1385.81027) Full Text: DOI arXiv
Marquette, Ian; Sajedi, Masoumeh; Winternitz, Pavel Fourth order superintegrable systems separating in Cartesian coordinates. I: Exotic quantum potentials. (English) Zbl 1447.70019 J. Phys. A, Math. Theor. 50, No. 31, Article ID 315201, 29 p. (2017). Reviewer: Christian Seifert (Hamburg) MSC: 70H06 33E17 34M55 81R12 PDFBibTeX XMLCite \textit{I. Marquette} et al., J. Phys. A, Math. Theor. 50, No. 31, Article ID 315201, 29 p. (2017; Zbl 1447.70019) Full Text: DOI arXiv
Levi, Decio; Martina, Luigi; Winternitz, Pavel Structure preserving discretizations of the Liouville equation and their numerical tests. (English) Zbl 1358.35072 SIGMA, Symmetry Integrability Geom. Methods Appl. 11, Paper 080, 20 p. (2015). MSC: 35L71 35A30 35L70 39A14 65N06 PDFBibTeX XMLCite \textit{D. Levi} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 11, Paper 080, 20 p. (2015; Zbl 1358.35072) Full Text: DOI arXiv EMIS
Riglioni, D.; Gingras, O.; Winternitz, P. Superintegrable systems with spin induced by co-algebra symmetry. (English) Zbl 1286.81108 J. Phys. A, Math. Theor. 47, No. 12, Article ID 122002, 12 p. (2014). MSC: 81R12 81Q05 81Q10 33C45 81Q80 PDFBibTeX XMLCite \textit{D. Riglioni} et al., J. Phys. A, Math. Theor. 47, No. 12, Article ID 122002, 12 p. (2014; Zbl 1286.81108) Full Text: DOI arXiv
Désilets, Jean-Francois; Winternitz, Pavel; Yurduşen, İsmet Superintegrable systems with spin and second-order integrals of motion. (English) Zbl 1258.81027 J. Phys. A, Math. Theor. 45, No. 46, Article ID 475201, 26 p. (2012). MSC: 81Q05 81R12 81U05 81V35 PDFBibTeX XMLCite \textit{J.-F. Désilets} et al., J. Phys. A, Math. Theor. 45, No. 46, Article ID 475201, 26 p. (2012; Zbl 1258.81027) Full Text: DOI arXiv
Post, Sarah; Winternitz, Pavel An infinite family of superintegrable deformations of the Coulomb potential. (English) Zbl 1190.81043 J. Phys. A, Math. Theor. 43, No. 22, Article ID 222001, 11 p. (2010). MSC: 81Q05 81R12 PDFBibTeX XMLCite \textit{S. Post} and \textit{P. Winternitz}, J. Phys. A, Math. Theor. 43, No. 22, Article ID 222001, 11 p. (2010; Zbl 1190.81043) Full Text: DOI arXiv
Tremblay, Frédérick; Winternitz, Pavel Third-order superintegrable systems separating in polar coordinates. (English) Zbl 1188.81108 J. Phys. A, Math. Theor. 43, No. 17, Article ID 175206, 17 p. (2010). MSC: 81R12 37J35 81Q05 33E05 33E17 PDFBibTeX XMLCite \textit{F. Tremblay} and \textit{P. Winternitz}, J. Phys. A, Math. Theor. 43, No. 17, Article ID 175206, 17 p. (2010; Zbl 1188.81108) Full Text: DOI arXiv
Winternitz, Pavel; Yurduşen, İsmet Integrable and superintegrable systems with spin in three-dimensional Euclidean space. (English) Zbl 1178.81112 J. Phys. A, Math. Theor. 42, No. 38, Article ID 385203, 20 p. (2009). MSC: 81R12 81V35 81Q05 33C45 PDFBibTeX XMLCite \textit{P. Winternitz} and \textit{İ. Yurduşen}, J. Phys. A, Math. Theor. 42, No. 38, Article ID 385203, 20 p. (2009; Zbl 1178.81112) Full Text: DOI arXiv
Winternitz, P.; Yurduşen, İ. Superintegrable systems with spin in two- and three-dimensional Euclidean spaces. (English) Zbl 1144.81467 Gaeta, Giuseppe (ed.) et al., Symmetry and perturbation theory. Proceedings of the 6th international conference, SPT 2007, Otranto, Italy, June 2–9, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-277-616-7/hbk). 215-222 (2008). MSC: 81R12 81Q05 PDFBibTeX XMLCite \textit{P. Winternitz} and \textit{İ. Yurduşen}, in: Symmetry and perturbation theory. Proceedings of the 6th international conference, SPT 2007, Otranto, Italy, June 2--9, 2007. Hackensack, NJ: World Scientific. 215--222 (2008; Zbl 1144.81467) Full Text: arXiv
Charest, F.; Hudon, C.; Winternitz, P. Quasiseparation of variables in the Schrödinger equation with a magnetic field. (English) Zbl 1121.81064 J. Math. Phys. 48, No. 1, 012105, 16 p. (2007). MSC: 81R12 35A30 35Q40 37K10 81Q05 PDFBibTeX XMLCite \textit{F. Charest} et al., J. Math. Phys. 48, No. 1, 012105, 16 p. (2007; Zbl 1121.81064) Full Text: DOI arXiv
Levi, Decio; Winternitz, Pavel Continuous symmetries of difference equations. (English) Zbl 1112.37053 J. Phys. A, Math. Gen. 39, No. 2, R1-R63 (2006). MSC: 37K05 35A30 39A11 39A12 65Q05 81R12 PDFBibTeX XMLCite \textit{D. Levi} and \textit{P. Winternitz}, J. Phys. A, Math. Gen. 39, No. 2, R1--R63 (2006; Zbl 1112.37053) Full Text: DOI arXiv
Levi, Decio; Tempesta, Piergiulio; Winternitz, Pavel Umbral calculus, difference equations and the discrete Schrödinger equation. (English) Zbl 1064.39020 J. Math. Phys. 45, No. 11, 4077-4105 (2004). MSC: 39A12 17B37 39A70 81Q05 81R12 PDFBibTeX XMLCite \textit{D. Levi} et al., J. Math. Phys. 45, No. 11, 4077--4105 (2004; Zbl 1064.39020) Full Text: DOI arXiv
Kalnins, E. G.; Kress, J. M.; Winternitz, P. Superintegrability in a two-dimensional space of nonconstant curvature. (English) Zbl 1059.37040 J. Math. Phys. 43, No. 2, 970-983 (2002). MSC: 37J35 70G45 70H06 70H20 81R12 PDFBibTeX XMLCite \textit{E. G. Kalnins} et al., J. Math. Phys. 43, No. 2, 970--983 (2002; Zbl 1059.37040) Full Text: DOI arXiv Link
Levi, D.; Tremblay, S.; Winternitz, P. Lie symmetries of multidimensional difference equations. (English) Zbl 0998.39008 J. Phys. A, Math. Gen. 34, No. 44, 9507-9524 (2001). MSC: 39A12 39A10 22E30 65M06 PDFBibTeX XMLCite \textit{D. Levi} et al., J. Phys. A, Math. Gen. 34, No. 44, 9507--9524 (2001; Zbl 0998.39008) Full Text: DOI arXiv
Winternitz, P. Bäcklund transformations as nonlinear ordinary differential, or difference equations with superposition formulas. (English) Zbl 0998.34005 Coley, Alan (ed.) et al., Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4-9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 29, 429-436 (2001). Reviewer: Werner M.Seiler (Mannheim) MSC: 34A25 34A26 22E60 34A05 PDFBibTeX XMLCite \textit{P. Winternitz}, in: Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4--9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. Providence, RI: American Mathematical Society (AMS). 429--436 (2001; Zbl 0998.34005)
Havlíček, M.; Pošta, S.; Winternitz, P. Superposition formulas based on nonprimitive group action. (English) Zbl 1004.34006 Coley, Alan (ed.) et al., Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4-9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 29, 225-231 (2001). Reviewer: G.Czichowski (Greifswald) MSC: 34A26 22E60 PDFBibTeX XMLCite \textit{M. Havlíček} et al., in: Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4--9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. Providence, RI: American Mathematical Society (AMS). 225--231 (2001; Zbl 1004.34006)
Sheftel, M. B.; Tempesta, P.; Winternitz, P. Superintegrable systems in quantum mechanics and classical Lie theory. (English) Zbl 1013.81020 J. Math. Phys. 42, No. 2, 659-673 (2001). MSC: 81R12 70S10 37K40 37N20 35Q51 PDFBibTeX XMLCite \textit{M. B. Sheftel} et al., J. Math. Phys. 42, No. 2, 659--673 (2001; Zbl 1013.81020) Full Text: DOI
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel Lie group classification of second-order ordinary difference equations. (English) Zbl 0981.39010 J. Math. Phys. 41, No. 1, 480-504 (2000). Reviewer: Peng Mingshu MSC: 39A12 22E99 34C14 PDFBibTeX XMLCite \textit{V. Dorodnitsyn} et al., J. Math. Phys. 41, No. 1, 480--504 (2000; Zbl 0981.39010) Full Text: DOI Link
Levi, D.; Tremblay, S.; Winternitz, P. Lie point symmetries of difference equations and lattices. (English) Zbl 0966.39007 J. Phys. A, Math. Gen. 33, No. 47, 8507-8523 (2000). Reviewer: Ondřej Došlý (Brno) MSC: 39A12 34C20 22E30 PDFBibTeX XMLCite \textit{D. Levi} et al., J. Phys. A, Math. Gen. 33, No. 47, 8507--8523 (2000; Zbl 0966.39007) Full Text: DOI arXiv
Hernández Heredero, R.; Levi, D.; Winternitz, P. Symmetry preserving discretization of the Burgers equation. (English) Zbl 0963.35168 Levi, Decio (ed.) et al., SIDE III - Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16-22, 1998. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 25, 197-208 (2000). MSC: 35Q53 37K30 22E70 39A12 PDFBibTeX XMLCite \textit{R. Hernández Heredero} et al., in: SIDE III -- Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16--22, 1998. Providence, RI: American Mathematical Society (AMS). 197--208 (2000; Zbl 0963.35168)
Martina, L.; Lafortune, S.; Winternitz, P. Point symmetries of generalized Toda field theories. II: Symmetry reduction. (English) Zbl 1064.37506 J. Phys. A, Math. Gen. 33, No. 36, 6431-6446 (2000). MSC: 37K10 37K05 37N20 81R12 37K60 81T40 PDFBibTeX XMLCite \textit{L. Martina} et al., J. Phys. A, Math. Gen. 33, No. 36, 6431--6446 (2000; Zbl 1064.37506) Full Text: DOI arXiv
Dorodnitsyn, Vladimir; Kozlov, Roman; Winternitz, Pavel On Lie group classification of second-order ordinary difference equations. (English) Zbl 0959.39017 Boiti, M. (ed.) et al., Proceedings of the workshop on nonlinearity, integrability and all that: twenty years after NEEDS ’79, Lecce, Italy, July 1-10, 1999. Singapore: World Scientific. 250-257 (2000). MSC: 39A12 34A26 22E05 PDFBibTeX XMLCite \textit{V. Dorodnitsyn} et al., in: Proceedings of the workshop on nonlinearity, integrability and all that: twenty years after NEEDS '79, Lecce, Italy, July 1--10, 1999. Singapore: World Scientific. 250--257 (2000; Zbl 0959.39017)
Thomova, Z.; Winternitz, P. Maximal abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces. (English) Zbl 0908.22018 J. Phys. A, Math. Gen. 31, No. 7, 1831-1858 (1998). Reviewer: A.Klimyk (Kyïv) MSC: 22E60 81R20 PDFBibTeX XMLCite \textit{Z. Thomova} and \textit{P. Winternitz}, J. Phys. A, Math. Gen. 31, No. 7, 1831--1858 (1998; Zbl 0908.22018) Full Text: DOI arXiv
Levi, D.; Vinet, L.; Winternitz, P. Lie group formalism for difference equations. (English) Zbl 0956.39013 J. Phys. A, Math. Gen. 30, No. 2, 633-649 (1997). Reviewer: Patricia J.Y.Wong (Singapore) MSC: 39A12 39A10 34C30 43A80 22E30 PDFBibTeX XMLCite \textit{D. Levi} et al., J. Phys. A, Math. Gen. 30, No. 2, 633--649 (1997; Zbl 0956.39013) Full Text: DOI
Levi, Decio; Winternitz, Pavel Lie point symmetries of differential difference equations. (English) Zbl 0860.22016 Levi, Decio (ed.) et al., Symmetries and integrability of difference equations. Papers from the workshop, May 22–29, 1994, Estérel, Canada. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 9, 199-208 (1996). Reviewer: A.Vaněček (Praha) MSC: 22E70 35A30 35Q53 PDFBibTeX XMLCite \textit{D. Levi} and \textit{P. Winternitz}, in: Symmetries and integrability of difference equations. Papers from the workshop, May 22--29, 1994, Estérel, Canada. Providence, RI: American Mathematical Society. 199--208 (1996; Zbl 0860.22016)
Winternitz, P.; Levi, D. Continuous symmetries of differential-difference equations. (English) Zbl 1102.35366 Bertrand, J. (ed.) et al., Modern group theoretical methods in physics. Proceedings of the conference in honour of Guy Rideau on the occasion of his retirement, Paris, France, January 1995. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-3645-3/hbk). Math. Phys. Stud. 18, 271-281 (1995). MSC: 35R10 35A30 58J70 PDFBibTeX XMLCite \textit{P. Winternitz} and \textit{D. Levi}, Math. Phys. Stud. 18, 271--281 (1995; Zbl 1102.35366) Full Text: DOI
Winternitz, P. Lie groups and solutions of nonlinear partial differential equations. (English) Zbl 0830.35004 Ibort, L. A. (ed.) et al., Integrable systems, quantum groups, and quantum field theories. Proceedings of the NATO Advanced Study Institute and XXIII GIFT international seminar on recent problems in mathematical physics, Salamanca, Spain, 15-27 June 1992. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 409, 429-495 (1993). Reviewer: P.Hillion (Le Vesinet) MSC: 35A30 58J70 22E70 35Q53 58J72 PDFBibTeX XMLCite \textit{P. Winternitz}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 409, 429--495 (1993; Zbl 0830.35004)
Levi, Decio; Winternitz, Pavel Symmetries of differential equations on a lattice. An example: The Toda lattice. (English) Zbl 0790.34005 Ibragimov, N. Kh. (ed.) et al., Modern group analysis: Advanced analytical and computational methods in mathematical physics. Proceedings of the international workshop Acireale, Catania, Italy, October 27-31, 1992. Dordrecht: Kluwer Academic Publishers. 265-272 (1993). MSC: 34A25 22E05 70H33 PDFBibTeX XMLCite \textit{D. Levi} and \textit{P. Winternitz}, in: Modern group analysis: Advanced analytical and computational methods in mathematical physics. Proceedings of the international workshop Acireale, Catania, Italy, October 27-31, 1992. Dordrecht: Kluwer Academic Publishers. 265--272 (1993; Zbl 0790.34005)
Gazeau, J. P.; Winternitz, P. Symmetries of variable coefficient Korteweg-de Vries equations. (English) Zbl 0767.35077 J. Math. Phys. 33, No. 12, 4087-4102 (1992). MSC: 35Q53 35A30 37J35 37K10 PDFBibTeX XMLCite \textit{J. P. Gazeau} and \textit{P. Winternitz}, J. Math. Phys. 33, No. 12, 4087--4102 (1992; Zbl 0767.35077) Full Text: DOI
Levi, D.; Nucci, M. C.; Rogers, C.; Winternitz, P. Group theoretical analysis of a rotating shallow liquid in a rigid container. (English) Zbl 0715.35067 J. Phys. A, Math. Gen. 22, No. 22, 4743-4767 (1989). MSC: 35Q35 35Q53 22E70 76B99 PDFBibTeX XMLCite \textit{D. Levi} et al., J. Phys. A, Math. Gen. 22, No. 22, 4743--4767 (1989; Zbl 0715.35067) Full Text: DOI
Gagnon, L.; Hussin, V.; Winternitz, P. Nonlinear equations with superposition formulas and exceptional group \(G_ 2\). III: The superposition formulas. (English) Zbl 0655.22015 J. Math. Phys. 29, No. 10, 2145-2155 (1988). MSC: 22E70 34G20 81T60 PDFBibTeX XMLCite \textit{L. Gagnon} et al., J. Math. Phys. 29, No. 10, 2145--2155 (1988; Zbl 0655.22015) Full Text: DOI
Beckers, J.; Hussin, V.; Winternitz, P. Nonlinear equations with superposition formulas and the exceptional groups \(G_ 2\). II: Classification of the equations. (English) Zbl 0614.22009 J. Math. Phys. 28, 520-529 (1987). MSC: 22E70 22E30 34G20 81T60 22E65 17B25 PDFBibTeX XMLCite \textit{J. Beckers} et al., J. Math. Phys. 28, 520--529 (1987; Zbl 0614.22009) Full Text: DOI
Beckers, J.; Hussin, V.; Winternitz, P. Nonlinear equations with superposition formulas and the exceptional group \(G_ 2\). I: Complex and real forms of \({\mathfrak g}_ 2\) and their maximal subalgebras. (English) Zbl 0614.22008 J. Math. Phys. 27, 2217-2227 (1986). MSC: 22E70 22E30 34G20 17B25 81T60 22E65 PDFBibTeX XMLCite \textit{J. Beckers} et al., J. Math. Phys. 27, 2217--2227 (1986; Zbl 0614.22008) Full Text: DOI
Winternitz, Pavel Lie groups and solutions of nonlinear differential equations. (English) Zbl 0571.34002 Nonlinear phenomena, Proc. CIFMO Sch. Workshop, Oaxtepec/Mex. 1982, Lect. Notes Phys. 189, 263-331 (1983). Reviewer: R.McGwier MSC: 34A05 35Q99 35A30 22E65 PDFBibTeX XML
Winternitz, P. Completely integrable Hamiltonian systems and the separation of variables. (English) Zbl 0528.58019 Group theoretical methods in physics, Proc. XIth int. Colloq., Istanbul 1982, Lect. Notes Phys. 180, 142-153 (1983). MSC: 37J35 37K10 35Q99 70H20 81R10 PDFBibTeX XML
Kramer, P. (ed.); Rieckers, A. (ed.) [Rittenberg, V.; Ferrara, S.; Kostant, Bertram; Kerber, A.; Primas, H.; Frei, H.; Günthard, H.; Sternberg, S.; Rowe, D. J.; Rosensteel, G.; Grossmann, A.; Kramer, P.; Birman, J. L.; Emch, G. G.; Michel, L.; Dürr, H. P.; van Leeuwen, J. M. J.; O’Raifeartaigh, L.; Albeverio, S.; Høegh-Krohn, Raphael; Backhouse, N.; Hoogland, H.; Patera, J.; Winternitz, P.; Zassenhaus, Hans; van den Broec, P. M.; Jaric, M. V.; Hughes, J. W. B.; King, R. C.; Qubanchi, A. H. A.] Group theoretical methods in physics. Sixth international colloquium, Tübingen 1977. (English) Zbl 0385.20001 Lecture Notes in Physics. 79. Berlin-Heidelberg-New York: Springer- Verlag. XVIII, 546 p. DM 47.00; $ 23.50 (1978). MSC: 20-06 81-02 81-06 81Txx 81T60 81V35 81S99 81P99 81V55 81R10 81Q10 17B70 17A70 17B10 53C15 53D50 43A65 20C35 22E50 81V70 82B26 82D25 46L60 35Q99 20H15 20G05 81V10 PDFBibTeX XML
Patera, J.; Sharp, R. T.; Winternitz, P.; Zassenhaus, Hans Subgroups of the Poincaré group and their invariants. (English) Zbl 0347.20029 J. Math. Phys. 17, 977-985 (1976). MSC: 20G45 70G99 35-00 PDFBibTeX XMLCite \textit{J. Patera} et al., J. Math. Phys. 17, 977--985 (1976; Zbl 0347.20029) Full Text: DOI