Masuda, Tetsu On additional symmetry and bilinearization of the \(q\)-Painlevé systems associated with the affine Weyl group of type \(A\). (English) Zbl 07790340 Lett. Math. Phys. 114, No. 1, Paper No. 9, 27 p. (2024). MSC: 17B80 34M55 37K35 39A13 PDFBibTeX XMLCite \textit{T. Masuda}, Lett. Math. Phys. 114, No. 1, Paper No. 9, 27 p. (2024; Zbl 07790340) Full Text: DOI
Lyu, Shulin; Chen, Yang; Xu, Shuai-Xia Laguerre unitary ensembles with jump discontinuities, PDEs and the coupled Painlevé V system. (English) Zbl 1518.35523 Physica D 449, Article ID 133755, 14 p. (2023). MSC: 35Q15 37K10 37K35 34M55 33C45 39A14 PDFBibTeX XMLCite \textit{S. Lyu} et al., Physica D 449, Article ID 133755, 14 p. (2023; Zbl 1518.35523) Full Text: DOI arXiv
Appel, Andrea; Gautam, Sachin; Wendlandt, Curtis The R-matrix of the affine Yangian. arXiv:2309.02377 Preprint, arXiv:2309.02377 [math.RT] (2023). MSC: 81R10 17B37 39A45 BibTeX Cite \textit{A. Appel} et al., ``The R-matrix of the affine Yangian'', Preprint, arXiv:2309.02377 [math.RT] (2023) Full Text: arXiv OA License
Nagao, Hidehito; Yamada, Yasuhiko Three \(q\)-Painlevé equations with affine Weyl group symmetry of type \(E_7^{(1)}\). arXiv:2304.08730 Preprint, arXiv:2304.08730 [nlin.SI] (2023). MSC: 14H70 34M55 37K20 39A13 BibTeX Cite \textit{H. Nagao} and \textit{Y. Yamada}, ``Three $q$-Painlev\'e equations with affine Weyl group symmetry of type $E_7^{(1)}$'', Preprint, arXiv:2304.08730 [nlin.SI] (2023) Full Text: arXiv OA License
Masuda, Tetsu; Okubo, Naoto; Tsuda, Teruhisa Cluster algebras and higher order generalizations of the \(q\)-Painleve equations of type \(A_7^{(1)}\) and \(A_6^{(1)}\). (English) Zbl 1517.13019 RIMS Kôkyûroku Bessatsu B87, 149-163 (2021). MSC: 13F60 20F55 34M55 37K10 39A13 PDFBibTeX XMLCite \textit{T. Masuda} et al., RIMS Kôkyûroku Bessatsu B87, 149--163 (2021; Zbl 1517.13019) Full Text: Link
Branquinho, Amílcar; Foulquié Moreno, Ana; Mañas, Manuel Matrix biorthogonal polynomials: eigenvalue problems and non-Abelian discrete Painlevé equations. A Riemann-Hilbert problem perspective. (English) Zbl 1458.37073 J. Math. Anal. Appl. 494, No. 2, Article ID 124605, 36 p. (2021). Reviewer: Vladimir P. Kostov (Nice) MSC: 37K20 37K60 39A36 37J70 37J65 33C47 33E17 34M55 34M50 15A16 PDFBibTeX XMLCite \textit{A. Branquinho} et al., J. Math. Anal. Appl. 494, No. 2, Article ID 124605, 36 p. (2021; Zbl 1458.37073) Full Text: DOI arXiv
Alfimov, G. L.; Korobeinikov, A. S.; Lustri, C. J.; Pelinovsky, D. E. Standing lattice solitons in the discrete NLS equation with saturation. (English) Zbl 1423.34019 Nonlinearity 32, No. 9, 3445-3484 (2019). MSC: 34A33 34M35 34M40 37K40 39A10 PDFBibTeX XMLCite \textit{G. L. Alfimov} et al., Nonlinearity 32, No. 9, 3445--3484 (2019; Zbl 1423.34019) Full Text: DOI arXiv
Joshi, Nalini Discrete Painlevé equations. (English) Zbl 1423.37003 CBMS Regional Conference Series in Mathematics 131. Providence, RI: American Mathematical Society (AMS), published for the Conference Board of the Mathematical Sciences (CBMS) (ISBN 978-1-4704-5038-0/pbk). vi, 146 p. (2019). Reviewer: Giuseppe Gaeta (Milano) MSC: 37-02 39-02 37K10 37J35 33E17 39A45 14E07 14E15 32S45 PDFBibTeX XMLCite \textit{N. Joshi}, Discrete Painlevé equations. Providence, RI: American Mathematical Society (AMS), published for the Conference Board of the Mathematical Sciences (CBMS) (2019; Zbl 1423.37003) Full Text: DOI arXiv
Nagao, Hidehito; Yamada, Yasuhiko Study of \(q\)-Garnier system by Padé method. (English) Zbl 1423.14218 Funkc. Ekvacioj, Ser. Int. 61, No. 1, 109-133 (2018). Reviewer: Vladimir P. Kostov (Nice) MSC: 14H70 33D15 33D70 34M55 37K20 39A13 39A20 41A05 41A20 41A21 PDFBibTeX XMLCite \textit{H. Nagao} and \textit{Y. Yamada}, Funkc. Ekvacioj, Ser. Int. 61, No. 1, 109--133 (2018; Zbl 1423.14218) Full Text: DOI arXiv
Stokes, Alexander Full-parameter discrete Painlevé systems from non-translational Cremona isometries. (English) Zbl 1411.34116 J. Phys. A, Math. Theor. 51, No. 49, Article ID 495206, 31 p. (2018). MSC: 34M55 14H70 14E07 33D52 39A12 39A10 37K10 37K35 PDFBibTeX XMLCite \textit{A. Stokes}, J. Phys. A, Math. Theor. 51, No. 49, Article ID 495206, 31 p. (2018; Zbl 1411.34116) Full Text: DOI arXiv
Ramani, A.; Grammaticos, B.; Tamizhmani, T. Investigating relations between discrete Painlevé equations: the multistep approach. (English) Zbl 1403.39006 J. Math. Phys. 59, No. 11, 113506, 10 p. (2018). MSC: 39A12 34M55 37J35 37K10 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Math. Phys. 59, No. 11, 113506, 10 p. (2018; Zbl 1403.39006) Full Text: DOI
Nakazono, Nobutaka Reduction of lattice equations to the Painlevé equations: \(\mathrm{P}_{\mathrm{IV}}\) and \(\mathrm{P}_{\mathrm{V}}\). (English) Zbl 1385.37080 J. Math. Phys. 59, No. 2, 022702, 18 p. (2018). MSC: 37K10 34M55 39A12 39A13 PDFBibTeX XMLCite \textit{N. Nakazono}, J. Math. Phys. 59, No. 2, 022702, 18 p. (2018; Zbl 1385.37080) Full Text: DOI arXiv
Nagao, Hidehito A variation of the \(q\)-Painlevé system with affine Weyl group symmetry of type \(E_7^{(1)}\). (English) Zbl 1387.14096 SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 092, 18 p. (2017). Reviewer: Vladimir P. Kostov (Nice) MSC: 14H70 33D15 33D70 34M55 37K20 39A13 41A21 PDFBibTeX XMLCite \textit{H. Nagao}, SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 092, 18 p. (2017; Zbl 1387.14096) Full Text: DOI arXiv
Willox, R.; Ramani, A.; Grammaticos, B. A systematic method for constructing discrete Painlevé equations in the degeneration cascade of the \(\operatorname{E}_8\) group. (English) Zbl 1391.37053 J. Math. Phys. 58, No. 12, 123504, 20 p. (2017). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37K10 34M55 39A12 20G41 PDFBibTeX XMLCite \textit{R. Willox} et al., J. Math. Phys. 58, No. 12, 123504, 20 p. (2017; Zbl 1391.37053) Full Text: DOI arXiv
Ramani, A.; Grammaticos, B.; Willox, R. Miura transformations for discrete Painlevé equations coming from the affine \(\operatorname{E}_{8}\) Weyl group. (English) Zbl 1365.39003 J. Math. Phys. 58, No. 4, 043502, 10 p. (2017). MSC: 39A12 34M55 37K35 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Math. Phys. 58, No. 4, 043502, 10 p. (2017; Zbl 1365.39003) Full Text: DOI arXiv
Kajiwara, Kenji; Noumi, Masatoshi; Yamada, Yasuhiko Geometric aspects of Painlevé equations. (English) Zbl 1441.34095 J. Phys. A, Math. Theor. 50, No. 7, Article ID 073001, 164 p. (2017). Reviewer: Vladimir P. Kostov (Nice) MSC: 34M55 14H70 33C20 33D15 37K20 39A10 39A13 PDFBibTeX XMLCite \textit{K. Kajiwara} et al., J. Phys. A, Math. Theor. 50, No. 7, Article ID 073001, 164 p. (2017; Zbl 1441.34095) Full Text: DOI arXiv
Grammaticos, B.; Ramani, A. Parameterless discrete Painlevé equations and their Miura relations. (English) Zbl 1420.34105 J. Nonlinear Math. Phys. 23, No. 1, 141-149 (2016). MSC: 34M55 37K10 39A12 34A25 37K35 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, J. Nonlinear Math. Phys. 23, No. 1, 141--149 (2016; Zbl 1420.34105) Full Text: DOI
Joshi, Nalini; Nakazono, Nobutaka Lax pairs of discrete Painlevé equations: \((A_2+A_1)^{(1)}\) case. (English) Zbl 1371.37125 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 472, No. 2196, Article ID 20160696, 14 p. (2016). MSC: 37K10 34M55 14H70 39A14 PDFBibTeX XMLCite \textit{N. Joshi} and \textit{N. Nakazono}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 472, No. 2196, Article ID 20160696, 14 p. (2016; Zbl 1371.37125) Full Text: DOI arXiv
Nagao, Hidehito Lax pairs for additive difference Painlevé equations. arXiv:1604.02530 Preprint, arXiv:1604.02530 [nlin.SI] (2016). MSC: 14H70 34M55 37K20 39A10 41A05 BibTeX Cite \textit{H. Nagao}, ``Lax pairs for additive difference Painlev\'e equations'', Preprint, arXiv:1604.02530 [nlin.SI] (2016) Full Text: arXiv OA License
Suzuki, Takao A \(q\)-analogue of the Drinfeld-Sokolov hierarchy of type \(A\) and \(q\)-Painlevé system. (English) Zbl 1346.39010 Dzhamay, Anton (ed.) et al., Algebraic and analytic aspects of integrable systems and Painlevé equations. AMS special session, Baltimore, MD, USA, January 18, 2014. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1654-6/pbk; 978-1-4704-2779-5/ebook). Contemporary Mathematics 651, 25-38 (2015). MSC: 39A12 39A13 34M55 37K10 37K35 33D15 PDFBibTeX XMLCite \textit{T. Suzuki}, Contemp. Math. 651, 25--38 (2015; Zbl 1346.39010) Full Text: DOI arXiv
Cheban, David Belitskii-Lyubich conjecture for \(C\)-analytic dynamical systems. (English) Zbl 1337.37059 Discrete Contin. Dyn. Syst., Ser. B 20, No. 3, 945-959 (2015). Reviewer: Matheus Cheque Bortolan (Lima) MSC: 37L15 37B25 34G20 34D05 34D23 39A45 PDFBibTeX XMLCite \textit{D. Cheban}, Discrete Contin. Dyn. Syst., Ser. B 20, No. 3, 945--959 (2015; Zbl 1337.37059) Full Text: DOI
Witte, N. S. Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy. (English) Zbl 1334.39024 Nagoya Math. J. 219, 127-234 (2015). Reviewer: Narahari Parhi (Bhubaneswar) MSC: 39A12 39A05 42C05 34M55 34M56 33C45 37K35 PDFBibTeX XMLCite \textit{N. S. Witte}, Nagoya Math. J. 219, 127--234 (2015; Zbl 1334.39024) Full Text: DOI arXiv
Liska, Sebastian; Colonius, Tim A parallel fast multipole method for elliptic difference equations. (English) Zbl 1349.65700 J. Comput. Phys. 278, 76-91 (2014). MSC: 65Q10 65N06 39A60 65B10 PDFBibTeX XMLCite \textit{S. Liska} and \textit{T. Colonius}, J. Comput. Phys. 278, 76--91 (2014; Zbl 1349.65700) Full Text: DOI arXiv Link
Ramani, A.; Grammaticos, B. Discrete Painlevé equations with maximal periodicities. (English) Zbl 1301.39005 J. Phys. A, Math. Theor. 47, No. 38, Article ID 385201, 7 p. (2014). MSC: 39A12 34M55 39A23 37J30 37K10 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, J. Phys. A, Math. Theor. 47, No. 38, Article ID 385201, 7 p. (2014; Zbl 1301.39005) Full Text: DOI
Dzhamay, Anton Combinatorics of matrix factorizations and integrable systems. (English) Zbl 1420.37104 J. Nonlinear Math. Phys. 20, Suppl. 1, 34-47 (2013). MSC: 37K35 34M56 39A10 37K20 PDFBibTeX XMLCite \textit{A. Dzhamay}, J. Nonlinear Math. Phys. 20, 34--47 (2013; Zbl 1420.37104) Full Text: DOI arXiv
Kanki, Masataka Integrability of discrete equations modulo a prime. (English) Zbl 1339.37053 SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 056, 8 p. (2013). MSC: 37K10 34M55 37P25 39A13 PDFBibTeX XMLCite \textit{M. Kanki}, SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 056, 8 p. (2013; Zbl 1339.37053) Full Text: DOI arXiv EMIS
Ikawa, Yusuke Hypergeometric solutions for the \(q\)-Painlevé equation of type \({E^{(1)}_6}\) by the Padé method. (English) Zbl 1280.39008 Lett. Math. Phys. 103, No. 7, 743-763 (2013). Reviewer: Jacques Sauloy (Toulouse) MSC: 39A13 41A21 34M55 37K35 PDFBibTeX XMLCite \textit{Y. Ikawa}, Lett. Math. Phys. 103, No. 7, 743--763 (2013; Zbl 1280.39008) Full Text: DOI arXiv
Ormerod, C. M.; van der Kamp, Peter H.; Quispel, G. R. W. Discrete Painlevé equations and their Lax pairs as reductions of integrable lattice equations. (English) Zbl 1266.39012 J. Phys. A, Math. Theor. 46, No. 9, Article ID 095204, 22 p. (2013). MSC: 39A14 39A12 37K15 34M55 35Q53 PDFBibTeX XMLCite \textit{C. M. Ormerod} et al., J. Phys. A, Math. Theor. 46, No. 9, Article ID 095204, 22 p. (2013; Zbl 1266.39012) Full Text: DOI arXiv
Kanki, Masataka Studies on the discrete integrable equations over finite fields. arXiv:1306.0962 Preprint, arXiv:1306.0962 [math-ph] (2013). MSC: 37K10 34M55 39A13 37P20 BibTeX Cite \textit{M. Kanki}, ``Studies on the discrete integrable equations over finite fields'', Preprint, arXiv:1306.0962 [math-ph] (2013) Full Text: arXiv OA License
Ormerod, Christopher M. Symmetries in connection preserving deformations. (English) Zbl 1219.39005 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 049, 13 p. (2011). MSC: 39A13 37K35 39A12 34M55 PDFBibTeX XMLCite \textit{C. M. Ormerod}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 049, 13 p. (2011; Zbl 1219.39005) Full Text: DOI arXiv EuDML
Ormerod, Christopher M. The lattice structure of connection preserving deformations for \(q\)-Painlevé equations I. (English) Zbl 1219.39004 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 045, 22 p. (2011). MSC: 39A13 34M55 37K35 39A12 PDFBibTeX XMLCite \textit{C. M. Ormerod}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 045, 22 p. (2011; Zbl 1219.39004) Full Text: DOI arXiv EuDML
Murata, M.; Satsuma, J.; Ramani, A.; Grammaticos, B. Discretising systematically the Painlevé equations. (English) Zbl 1217.37059 Physica D 240, No. 3, 305-309 (2011). Reviewer: Johanna Michor (Wien) MSC: 37K10 34M55 39A12 PDFBibTeX XMLCite \textit{M. Murata} et al., Physica D 240, No. 3, 305--309 (2011; Zbl 1217.37059) Full Text: DOI
Tsuda, Teruhisa On an integrable system of \(q\)-difference equations satisfied by the universal characters: its Lax formalism and an application to \(q\)-Painlevé equations. (English) Zbl 1215.39010 Commun. Math. Phys. 293, No. 2, 347-359 (2010). Reviewer: Ahmed Hegazi (Mansoura) MSC: 39A13 37K10 37K60 39A12 34M55 33E17 PDFBibTeX XMLCite \textit{T. Tsuda}, Commun. Math. Phys. 293, No. 2, 347--359 (2010; Zbl 1215.39010) Full Text: DOI arXiv
Ramani, A.; Grammaticos, B.; Joshi, N. Second-degree discrete Painlevé equations conceal first-degree ones. (English) Zbl 1190.39003 J. Phys. A, Math. Theor. 43, No. 17, Article ID 175207, 9 p. (2010). MSC: 39A12 37K10 34M55 11C08 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 43, No. 17, Article ID 175207, 9 p. (2010; Zbl 1190.39003) Full Text: DOI
Pickering, Andrew Bäcklund transformations for a discrete second Painlevé hierarchy. (English) Zbl 1200.39007 J. Math. Phys. 50, No. 1, 013507, 6 p. (2009). MSC: 39A99 34M55 37K35 PDFBibTeX XMLCite \textit{A. Pickering}, J. Math. Phys. 50, No. 1, 013507, 6 p. (2009; Zbl 1200.39007) Full Text: DOI
Dzhamay, Anton Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painlevé equations. (English) Zbl 1181.15016 J. Phys. A, Math. Theor. 42, No. 45, Article ID 454008, 10 p. (2009). Reviewer: Ondřej Došlý (Brno) MSC: 15A23 39A10 37K20 39A12 34M55 15A54 PDFBibTeX XMLCite \textit{A. Dzhamay}, J. Phys. A, Math. Theor. 42, No. 45, Article ID 454008, 10 p. (2009; Zbl 1181.15016) Full Text: DOI arXiv
Tsuda, Teruhisa Universal character and \(q\)-difference Painlevé equations. (English) Zbl 1193.34177 Math. Ann. 345, No. 2, 395-415 (2009). Reviewer: Jacques Sauloy (Toulouse) MSC: 34M55 37K10 39A13 PDFBibTeX XMLCite \textit{T. Tsuda}, Math. Ann. 345, No. 2, 395--415 (2009; Zbl 1193.34177) Full Text: DOI
Arinkin, D.; Borodin, A. \(\tau \)-function of discrete isomonodromy transformations and probability. (English) Zbl 1210.14036 Compos. Math. 145, No. 3, 747-772 (2009). MSC: 14H70 37K20 39A45 60B20 PDFBibTeX XMLCite \textit{D. Arinkin} and \textit{A. Borodin}, Compos. Math. 145, No. 3, 747--772 (2009; Zbl 1210.14036) Full Text: DOI arXiv
Tsuda, Teruhisa A geometric approach to tau-functions of difference Painlevé equations. (English) Zbl 1173.39003 Lett. Math. Phys. 85, No. 1, 65-78 (2008). Reviewer: Miloš Čanak (Beograd) MSC: 39A10 34M55 39A12 14E05 33E17 37K20 37K35 PDFBibTeX XMLCite \textit{T. Tsuda}, Lett. Math. Phys. 85, No. 1, 65--78 (2008; Zbl 1173.39003) Full Text: DOI arXiv
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.; Tamizhmani, T. Painlevé equations: from continuous to discrete. (English) Zbl 1190.34117 Proc. Natl. Acad. Sci. India, Sect. A, Phys. Sci. 78, No. 2, 85-104 (2008). Reviewer: Svitlana P. Rogovchenko (Umeå) MSC: 34M55 37K10 39A12 PDFBibTeX XMLCite \textit{K. M. Tamizhmani} et al., Proc. Natl. Acad. Sci. India, Sect. A, Phys. Sci. 78, No. 2, 85--104 (2008; Zbl 1190.34117)
Nagoya, Hajime Quantum Painlevé systems of type \(A_{n-1}^{(1)}\) with higher degree Lax operators. (English) Zbl 1123.34070 Int. J. Math. 18, No. 7, 839-868 (2007). MSC: 34M55 37K35 81S99 39A99 PDFBibTeX XMLCite \textit{H. Nagoya}, Int. J. Math. 18, No. 7, 839--868 (2007; Zbl 1123.34070) Full Text: DOI
Tsuda, Teruhisa Tropical Weyl group action via point configurations and \(\tau\)-functions of the \(q\)-Painlevé equations. (English) Zbl 1118.39007 Lett. Math. Phys. 77, No. 1, 21-30 (2006). Reviewer: Ahmed Hegazi (Mansoura) MSC: 39A13 34M55 37K20 37K35 17B20 20F55 PDFBibTeX XMLCite \textit{T. Tsuda}, Lett. Math. Phys. 77, No. 1, 21--30 (2006; Zbl 1118.39007) Full Text: DOI
Tsuda, Teruhisa Tau functions of \(q\)-Painlevé III and IV equations. (English) Zbl 1119.39018 Lett. Math. Phys. 75, No. 1, 39-47 (2006). Reviewer: Jacques Sauloy (Toulouse) MSC: 39A13 34M55 37K10 PDFBibTeX XMLCite \textit{T. Tsuda}, Lett. Math. Phys. 75, No. 1, 39--47 (2006; Zbl 1119.39018) Full Text: DOI
Sakka, A.; Muğan, U. Bäcklund transformations for discrete Painlevé equations: discrete P\(_{\text{II}}\)-P\(_{\text{V}}\). (English) Zbl 1096.39020 Chaos Solitons Fractals 27, No. 2, 387-394 (2006). Reviewer: Ayşe Karasu (Ankara) MSC: 39A12 34M55 34M25 37K35 PDFBibTeX XMLCite \textit{A. Sakka} and \textit{U. Muğan}, Chaos Solitons Fractals 27, No. 2, 387--394 (2006; Zbl 1096.39020) Full Text: DOI
Reich, Ludwig; Smítal, Jaroslav; Štefánková, Marta Local analytic solutions of the generalized Dhombres functional equation. I. (English) Zbl 1117.39015 Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 214, 3-25 (2005). Reviewer: Zsolt Páles (Debrecen) MSC: 39B12 39B32 30D05 34M55 PDFBibTeX XMLCite \textit{L. Reich} et al., Sitzungsber., Abt. II, Österr. Akad. Wiss., Math.-Naturwiss. Kl. 214, 3--25 (2005; Zbl 1117.39015) Full Text: DOI
Tsuda, Teruhisa Universal characters and \(q\)-Painlevé systems. (English) Zbl 1093.39020 Commun. Math. Phys. 260, No. 1, 59-73 (2005). Reviewer: Jacques Sauloy (Toulouse) MSC: 39A13 39A12 37K10 34M55 PDFBibTeX XMLCite \textit{T. Tsuda}, Commun. Math. Phys. 260, No. 1, 59--73 (2005; Zbl 1093.39020) Full Text: DOI
Grammaticos, B.; Ramani, A. Generating discrete Painlevé equations from affine Weyl groups. (English) Zbl 1119.39301 Regul. Chaotic Dyn. 10, No. 2, 145-152 (2005). MSC: 39A12 34M55 37K35 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, Regul. Chaotic Dyn. 10, No. 2, 145--152 (2005; Zbl 1119.39301) Full Text: DOI Link
Joshi, N.; Nijhoff, F. W.; Ormerod, C. Lax pairs for ultra-discrete Painlevé cellular automata. (English) Zbl 1071.39019 J. Phys. A, Math. Gen. 37, No. 44, L559-L565 (2004). Reviewer: Edwin Engin Yaz (Milwaukee) MSC: 39A12 33E17 37B15 37K10 34M55 PDFBibTeX XMLCite \textit{N. Joshi} et al., J. Phys. A, Math. Gen. 37, No. 44, L559--L565 (2004; Zbl 1071.39019) Full Text: DOI
Tamizhmani, K. M.; Tamizhmani, T.; Grammaticos, B.; Ramani, A. Special solutions for discrete Painlevé equations. (English) Zbl 1064.39021 Grammaticos, B. (ed.) et al., Discrete integrable systems. Proceedings of the international CIMPA school, Pondicherry, India, February 2–14, 2003. Berlin: Springer (ISBN 3-540-21425-9/hbk). Lecture Notes in Physics 644, 323-382 (2004). MSC: 39A12 34M55 33E17 37K35 PDFBibTeX XMLCite \textit{K. M. Tamizhmani} et al., Lect. Notes Phys. 644, 323--382 (2004; Zbl 1064.39021)
Nagoya, Hajime Quantum Painlevé systems of type\(A^{(1)}_l\). (English) Zbl 1066.34087 Int. J. Math. 15, No. 10, 1007-1031 (2004). MSC: 34M55 37K35 39A99 81S99 PDFBibTeX XMLCite \textit{H. Nagoya}, Int. J. Math. 15, No. 10, 1007--1031 (2004; Zbl 1066.34087) Full Text: DOI arXiv
Lafortune, S.; Goriely, A. Singularity confinement and algebraic integrability. (English) Zbl 1070.37039 J. Math. Phys. 45, No. 3, 1191-1208 (2004). MSC: 37J35 39A12 34M55 37K10 PDFBibTeX XMLCite \textit{S. Lafortune} and \textit{A. Goriely}, J. Math. Phys. 45, No. 3, 1191--1208 (2004; Zbl 1070.37039) Full Text: DOI arXiv Link
Murata, Mikio; Sakai, Hidetaka; Yoneda, Jin Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type \(E^{(1)}_8\). (English) Zbl 1062.34102 J. Math. Phys. 44, No. 3, 1396-1414 (2003). MSC: 34M55 37K20 39A12 PDFBibTeX XMLCite \textit{M. Murata} et al., J. Math. Phys. 44, No. 3, 1396--1414 (2003; Zbl 1062.34102) Full Text: DOI arXiv
Carstea, A. S.; Ramani, A.; Willox, R.; Grammaticos, B. The discrete Painlevé II equations: Miura and auto-Bäcklund transformations. (English) Zbl 1049.39021 J. Phys. A, Math. Gen. 36, No. 31, 8419-8431 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 39A12 34M55 37K35 PDFBibTeX XMLCite \textit{A. S. Carstea} et al., J. Phys. A, Math. Gen. 36, No. 31, 8419--8431 (2003; Zbl 1049.39021) Full Text: DOI
Grammaticos, B.; Tamizhmani, T.; Ramani, A.; Carstea, A. S.; Tamizhmani, K. M. A bilinear approach to the discrete Painlevé I equations. (English) Zbl 1074.39023 J. Phys. Soc. Japan 71, No. 2, 443-447 (2002). MSC: 39A13 39A12 34M55 37K10 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Phys. Soc. Japan 71, No. 2, 443--447 (2002; Zbl 1074.39023) Full Text: DOI
Tokihiro, T.; Grammaticos, B.; Ramani, A. From the continuous P\(_{\text{V}}\) to discrete Painlevé equations. (English) Zbl 1046.39013 J. Phys. A, Math. Gen. 35, No. 28, 5943-5950 (2002). MSC: 39A12 33E17 34M55 37K35 PDFBibTeX XMLCite \textit{T. Tokihiro} et al., J. Phys. A, Math. Gen. 35, No. 28, 5943--5950 (2002; Zbl 1046.39013) Full Text: DOI
Kajiwara, Kenji; Noumi, Masatoshi; Yamada, Yasuhiko \(q\)-Painlevé systems arising from \(q\)-KP hierarchy. (English) Zbl 1030.37045 Lett. Math. Phys. 62, No. 3, 259-268 (2002). Reviewer: Ondřej Došlý (Brno) MSC: 37K10 39A13 34M55 37K35 PDFBibTeX XMLCite \textit{K. Kajiwara} et al., Lett. Math. Phys. 62, No. 3, 259--268 (2002; Zbl 1030.37045) Full Text: DOI arXiv
Kudryashov, N. A.; Soukharev, M. B. Discrete equations corresponding to fourth-order differential equations of the \(P_2\) and \(K_2\) hierarchies. (English) Zbl 1056.34102 ANZIAM J. 44, No. 1, 149-160 (2002). Reviewer: Mingshu Peng (Beijing) MSC: 34M55 39A12 37K10 PDFBibTeX XMLCite \textit{N. A. Kudryashov} and \textit{M. B. Soukharev}, ANZIAM J. 44, No. 1, 149--160 (2002; Zbl 1056.34102) Full Text: DOI
Noumi, M. Affine Weyl group approach to Painlevé equations. (English) Zbl 1014.34079 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press. 497-509 (2002). Reviewer: Shun Shimomura (Yokohama) MSC: 34M55 37K35 39A12 PDFBibTeX XMLCite \textit{M. Noumi}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. III: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 497--509 (2002; Zbl 1014.34079) Full Text: arXiv
Kajiwara, Kenji; Noumi, Masatoshi; Yamada, Yasuhiko Discrete dynamical systems with \(W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})\) symmetry. (English) Zbl 1077.37046 Lett. Math. Phys. 60, No. 3, 211-219 (2002). MSC: 37K60 34M55 37K05 37K35 39A13 PDFBibTeX XMLCite \textit{K. Kajiwara} et al., Lett. Math. Phys. 60, No. 3, 211--219 (2002; Zbl 1077.37046) Full Text: DOI arXiv
Grammaticos, B.; Tamizhmani, T.; Ramani, A.; Tamizhmani, K. M. Growth and integrability in discrete systems. (English) Zbl 1006.39018 J. Phys. A, Math. Gen. 34, No. 18, 3811-3821 (2001). Reviewer: Nicolae Cotfas (Bucureşti) MSC: 39A12 37K10 34M55 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Phys. A, Math. Gen. 34, No. 18, 3811--3821 (2001; Zbl 1006.39018) Full Text: DOI
Conte, Robert; Musette, Micheline Towards second order Lax pairs to discrete Painlevé equations of first degree. (English) Zbl 1115.37343 Chaos Solitons Fractals 11, No. 1-3, 41-52 (2000). MSC: 37K10 34M55 39A12 PDFBibTeX XMLCite \textit{R. Conte} and \textit{M. Musette}, Chaos Solitons Fractals 11, No. 1--3, 41--52 (2000; Zbl 1115.37343) Full Text: DOI arXiv
Grammaticos, B.; Ramani, A. Integrability in a discrete world. (English) Zbl 1115.37344 Chaos Solitons Fractals 11, No. 1-3, 7-18 (2000). MSC: 37K10 34M55 39A12 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, Chaos Solitons Fractals 11, No. 1--3, 7--18 (2000; Zbl 1115.37344) Full Text: DOI
Klarkson, P. A.; Mansfield, E. L.; Webster, H. N. On the relation between the continuous and discrete Painlevé equations. (English. Russian original) Zbl 0994.34077 Theor. Math. Phys. 122, No. 1, 1-16 (2000); translation from Teor. Mat. Fiz. 122, No. 1, 5-22 (2000). Reviewer: Juan J.Morales-Ruiz (Barcelona) MSC: 34M55 39A12 37K10 PDFBibTeX XMLCite \textit{P. A. Klarkson} et al., Theor. Math. Phys. 122, No. 1, 5--22 (2000; Zbl 0994.34077); translation from Teor. Mat. Fiz. 122, No. 1, 5--22 (2000)
Estévez, P. G.; Clarkson, P. A. Discrete equations and the singular manifold method. (English) Zbl 0958.37057 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, 139-146 (2000). MSC: 37K35 34M55 39A10 PDFBibTeX XMLCite \textit{P. G. Estévez} and \textit{P. A. Clarkson}, 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). 139--146 (2000; Zbl 0958.37057) Full Text: arXiv
Ramani, A.; Ohta, Y.; Grammaticos, B. Discrete integrable systems from continuous Painlevé equations through limiting procedures. (English) Zbl 0963.37069 Nonlinearity 13, No. 4, 1073-1085 (2000). MSC: 37K15 39A12 35Q51 37K60 34M55 PDFBibTeX XMLCite \textit{A. Ramani} et al., Nonlinearity 13, No. 4, 1073--1085 (2000; Zbl 0963.37069) Full Text: DOI
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M. Deautonomisation of differential-difference equations and discrete Painlevé equations. (English) Zbl 0952.37039 Chaos Solitons Fractals 11, No. 5, 757-764 (2000). Reviewer: Samir Musayev (Baku) MSC: 37K10 39A12 34K99 34M55 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., Chaos Solitons Fractals 11, No. 5, 757--764 (2000; Zbl 0952.37039) Full Text: DOI
Nijhoff, Frank; Joshi, Nalini; Hone, Andrew On the discrete and continuous Miura chain associated with the sixth Painlevé equation. (English) Zbl 0944.37041 Phys. Lett., A 264, No. 5, 396-406 (2000). MSC: 37K15 37K20 37K10 34M55 39A12 PDFBibTeX XMLCite \textit{F. Nijhoff} et al., Phys. Lett., A 264, No. 5, 396--406 (2000; Zbl 0944.37041) Full Text: DOI arXiv
Agafonov, Sergey I.; Bobenko, Alexander I. Discrete \(Z^\gamma\) and Painlevé equations. (English) Zbl 0969.39015 Int. Math. Res. Not. 2000, No. 4, 165-193 (2000). Reviewer: Serguei Zelik (Moskva) MSC: 39A12 37K10 34M55 30C20 PDFBibTeX XMLCite \textit{S. I. Agafonov} and \textit{A. I. Bobenko}, Int. Math. Res. Not. 2000, No. 4, 165--193 (2000; Zbl 0969.39015) Full Text: DOI
Ohta, Yasuhiro Self-dual construction of discrete Painlevé equations. (Japanese) Zbl 0951.39502 RIMS Kokyuroku 1098, 130-137 (1999). MSC: 39A12 34M55 37K10 PDFBibTeX XMLCite \textit{Y. Ohta}, RIMS Kokyuroku 1098, 130--137 (1999; Zbl 0951.39502)
Clarkson, Peter A.; Bassom, Andrew P. Bäcklund transformations and hierarchies of exact solutions for the fourth Painlevé equation and their application to discrete equations. (English) Zbl 0862.34003 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, 63-77 (1996). MSC: 34M55 34A05 33E30 58E07 33C45 34A34 37K35 34A25 39A10 PDFBibTeX XMLCite \textit{P. A. Clarkson} and \textit{A. P. Bassom}, in: Symmetries and integrability of difference equations. Papers from the workshop, May 22--29, 1994, Estérel, Canada. Providence, RI: American Mathematical Society. 63--77 (1996; Zbl 0862.34003) Full Text: arXiv
Berenstein, Carlos A.; Sebbar, Ahmed Monodromic differential equations and Riemann theta functions. (English) Zbl 0787.30002 Forum Math. 6, No. 2, 153-181 (1994). MSC: 30D05 34M35 34A35 39A05 30B40 PDFBibTeX XMLCite \textit{C. A. Berenstein} and \textit{A. Sebbar}, Forum Math. 6, No. 2, 153--181 (1994; Zbl 0787.30002) Full Text: DOI EuDML
Strambach, Karl Multiplikationen mit großen Automorphismengruppen. (Multiplications having a big group of automorphisms). (German) Zbl 0633.20052 Aequationes Math. 32, 311-326 (1987). Reviewer: H.Szambien MSC: 20N99 51A30 20B27 39B99 51J05 20B22 22A30 PDFBibTeX XMLCite \textit{K. Strambach}, Aequationes Math. 32, 311--326 (1987; Zbl 0633.20052) Full Text: DOI EuDML