Um, D.; Ramani, A.; Grammaticos, B.; Willox, R.; Satsuma, J. On the singularities of the discrete Korteweg-deVries equation. (English) Zbl 1519.37102 J. Phys. A, Math. Theor. 54, No. 9, Article ID 095201, 26 p. (2021). MSC: 37K60 39A36 35Q53 PDFBibTeX XMLCite \textit{D. Um} et al., J. Phys. A, Math. Theor. 54, No. 9, Article ID 095201, 26 p. (2021; Zbl 1519.37102) Full Text: DOI arXiv
Um, Doyong; Willox, Ralph; Grammaticos, Basil; Ramani, Alfred On the singularity structure of the discrete KdV equation. (English) Zbl 1514.39012 J. Phys. A, Math. Theor. 53, No. 11, Article ID 114001, 24 p. (2020). MSC: 39A36 39A12 35Q53 37K60 PDFBibTeX XMLCite \textit{D. Um} et al., J. Phys. A, Math. Theor. 53, No. 11, Article ID 114001, 24 p. (2020; Zbl 1514.39012) Full Text: DOI arXiv
Grammaticos, B.; Ramani, A.; Willox, R.; Satsuma, J. Discrete Painlevé equations from singularity patterns: the asymmetric trihomographic case. (English) Zbl 1441.39013 J. Math. Phys. 61, No. 3, 033503, 20 p. (2020). Reviewer: Eszter Gselmann (Debrecen) MSC: 39A36 37J70 39A12 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Math. Phys. 61, No. 3, 033503, 20 p. (2020; Zbl 1441.39013) Full Text: DOI arXiv
Mase, Takafumi; Willox, Ralph; Ramani, Alfred; Grammaticos, Basil Singularity confinement as an integrability criterion. (English) Zbl 1509.39014 J. Phys. A, Math. Theor. 52, No. 20, Article ID 205201, 29 p. (2019). MSC: 39A36 37J70 37K60 PDFBibTeX XMLCite \textit{T. Mase} et al., J. Phys. A, Math. Theor. 52, No. 20, Article ID 205201, 29 p. (2019; Zbl 1509.39014) Full Text: DOI arXiv
Grammaticos, B.; Ramani, A.; Willox, R. Restoring discrete Painlevé equations from an \(\mathrm{E}_8^{(1)}\)-associated one. (English) Zbl 1416.39003 J. Math. Phys. 60, No. 6, 063502, 16 p. (2019). MSC: 39A12 39A10 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Math. Phys. 60, No. 6, 063502, 16 p. (2019; Zbl 1416.39003) Full Text: DOI arXiv
Ramani, A.; Grammaticos, B.; Satsuma, J.; Tamizhmani, T. On the canonical forms of QRT mappings and discrete Painlevé equations. (English) Zbl 1406.39007 J. Phys. A, Math. Theor. 51, No. 39, Article ID 395203, 14 p. (2018). MSC: 39A12 39A05 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 51, No. 39, Article ID 395203, 14 p. (2018; Zbl 1406.39007) Full Text: DOI
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
Mase, T.; Willox, R.; Ramani, A.; Grammaticos, B. Integrable mappings and the notion of anticonfinement. (English) Zbl 1405.37063 J. Phys. A, Math. Theor. 51, No. 26, Article ID 265201, 11 p. (2018). MSC: 37J35 39A12 PDFBibTeX XMLCite \textit{T. Mase} et al., J. Phys. A, Math. Theor. 51, No. 26, Article ID 265201, 11 p. (2018; Zbl 1405.37063) Full Text: DOI arXiv
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Satsuma, J. Calculating the algebraic entropy of mappings with unconfined singularities. (English) Zbl 1397.37062 J. Integrable Syst. 3, Article ID xyy006, 16 p. (2018). MSC: 37J35 37K10 39A12 28D20 14E05 32H50 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Integrable Syst. 3, Article ID xyy006, 16 p. (2018; Zbl 1397.37062) 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
Grammaticos, B.; Ramani, A.; Willox, R.; Satsuma, J. Multiplicative equations related to the affine Weyl group \(\mathrm{E}_8\). (English) Zbl 1373.39005 J. Math. Phys. 58, No. 8, 083502, 9 p. (2017). MSC: 39A12 34M55 14L17 33E05 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Math. Phys. 58, No. 8, 083502, 9 p. (2017; Zbl 1373.39005) 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
Tamizhmani, K. M.; Tamizhmani, T.; Ramani, A.; Grammaticos, B. On the limits of discrete Painlevé equations associated with the affine Weyl group \(E_{8}\). (English) Zbl 1362.39017 J. Math. Phys. 58, No. 3, 033506, 11 p. (2017). MSC: 39A12 34M55 14L17 PDFBibTeX XMLCite \textit{K. M. Tamizhmani} et al., J. Math. Phys. 58, No. 3, 033506, 11 p. (2017; Zbl 1362.39017) Full Text: DOI
Ramani, A.; Grammaticos, B. Singularity analysis for difference Painlevé equations associated with the affine Weyl group \(E_8\). (English) Zbl 1359.39005 J. Phys. A, Math. Theor. 50, No. 5, Article ID 055204, 18 p. (2017). MSC: 39A12 34M55 39A20 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, J. Phys. A, Math. Theor. 50, No. 5, Article ID 055204, 18 p. (2017; Zbl 1359.39005) Full Text: DOI
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
Grammaticos, B.; Ramani, A. From trihomographic to elliptic Painlevé equations. (English) Zbl 1354.39005 J. Phys. A, Math. Theor. 49, No. 45, Article ID 45LT02, 10 p. (2016). MSC: 39A12 34M55 39A20 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, J. Phys. A, Math. Theor. 49, No. 45, Article ID 45LT02, 10 p. (2016; Zbl 1354.39005) Full Text: DOI
Willox, R.; Mase, T.; Ramani, A.; Grammaticos, B. Full-deautonomisation of a lattice equation. (English) Zbl 1353.37138 J. Phys. A, Math. Theor. 49, No. 28, Article ID 28LT01, 11 p. (2016). Reviewer: Ti-Jun Xiao (Fudan) MSC: 37K10 39A12 PDFBibTeX XMLCite \textit{R. Willox} et al., J. Phys. A, Math. Theor. 49, No. 28, Article ID 28LT01, 11 p. (2016; Zbl 1353.37138) Full Text: DOI arXiv
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J. Strongly asymmetric discrete Painlevé equations: the multiplicative case. (English) Zbl 1383.39019 J. Math. Phys. 57, No. 4, 043506, 30 p. (2016). MSC: 39A60 34M55 34B20 39A20 39A23 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Math. Phys. 57, No. 4, 043506, 30 p. (2016; Zbl 1383.39019) Full Text: DOI
Ramani, Alfred; Grammaticos, Basile A class of integrable non-QRT mappings and their deautonomisation. (English) Zbl 1333.37083 Lett. Math. Phys. 106, No. 3, 433-444 (2016). MSC: 37J35 39A10 39A13 58K20 37A35 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, Lett. Math. Phys. 106, No. 3, 433--444 (2016; Zbl 1333.37083) Full Text: DOI
Mase, T.; Willox, R.; Grammaticos, B.; Ramani, A. Deautonomization by singularity confinement: an algebro-geometric justification. (English) Zbl 1371.39011 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 471, No. 2183, Article ID 20140956, 20 p. (2015). MSC: 39A12 14D05 34M55 PDFBibTeX XMLCite \textit{T. Mase} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 471, No. 2183, Article ID 20140956, 20 p. (2015; Zbl 1371.39011) Full Text: DOI arXiv
Grammaticos, B.; Ramani, A.; Willox, R.; Mase, T.; Satsuma, J. Singularity confinement and full-deautonomisation: a discrete integrability criterion. (English) Zbl 1364.39001 Physica D 313, 11-25 (2015). MSC: 39A05 14J26 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., Physica D 313, 11--25 (2015; Zbl 1364.39001) Full Text: DOI arXiv
Ramani, A.; Grammaticos, B. Discrete Painlevé equations associated with the affine Weyl group \(E_{8}\). (English) Zbl 1326.39006 J. Phys. A, Math. Theor. 48, No. 35, Article ID 355204, 14 p. (2015). MSC: 39A12 34M55 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, J. Phys. A, Math. Theor. 48, No. 35, Article ID 355204, 14 p. (2015; Zbl 1326.39006) Full Text: DOI
Grammaticos, B.; Ramani, A. On a novel representation of discrete Painlevé equations. (English) Zbl 1323.39004 J. Math. Phys. 56, No. 8, 083507, 13 p. (2015). MSC: 39A12 34M55 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, J. Math. Phys. 56, No. 8, 083507, 13 p. (2015; Zbl 1323.39004) Full Text: DOI
Grammaticos, B.; Ramani, A. Elliptic and multiplicative discrete Painlevé equations from the affine Weyl group \(E_{8}\). (English) Zbl 1315.39002 J. Phys. A, Math. Theor. 48, No. 16, Article ID 16FT02, 16 p. (2015). MSC: 39A12 34M55 39A10 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, J. Phys. A, Math. Theor. 48, No. 16, Article ID 16FT02, 16 p. (2015; Zbl 1315.39002) Full Text: DOI
Ramani, A.; Grammaticos, B.; Willox, R.; Mase, T.; Kanki, M. The redemption of singularity confinement. (English) Zbl 1312.37043 J. Phys. A, Math. Theor. 48, No. 11, Article ID 11FT02, 8 p. (2015). MSC: 37K10 39A12 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 48, No. 11, Article ID 11FT02, 8 p. (2015; Zbl 1312.37043) Full Text: DOI arXiv
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
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J. Strongly asymmetric discrete Painlevé equations: the additive case. (English) Zbl 1295.39003 J. Math. Phys. 55, No. 5, 053503, 17 p. (2014). MSC: 39A12 39A10 34M55 37J15 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Math. Phys. 55, No. 5, 053503, 17 p. (2014; Zbl 1295.39003) Full Text: DOI
Ramani, A.; Grammaticos, B. On two discrete Painlevé equations with high periodicities. (English) Zbl 1291.39017 J. Phys. A, Math. Theor. 47, No. 19, Article ID 192001, 8 p. (2014). MSC: 39A12 39A20 34M55 39A23 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, J. Phys. A, Math. Theor. 47, No. 19, Article ID 192001, 8 p. (2014; Zbl 1291.39017) Full Text: DOI
Ramani, A.; Grammaticos, B. A new family of discrete Painlevé equations and associated linearisable systems. (English) Zbl 1420.37085 J. Nonlinear Math. Phys. 20, Suppl. 1, 153-164 (2013). MSC: 37K10 39A12 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, J. Nonlinear Math. Phys. 20, 153--164 (2013; Zbl 1420.37085) Full Text: DOI
Mimura, N.; Satsuma, J.; Ramani, A.; Grammaticos, B. Linearisable ultradiscrete systems with sign variables and the confinement of singularities. (English) Zbl 1283.39004 J. Math. Phys. 54, No. 2, 023504, 30 p. (2013). MSC: 39A12 34M35 PDFBibTeX XMLCite \textit{N. Mimura} et al., J. Math. Phys. 54, No. 2, 023504, 30 p. (2013; Zbl 1283.39004) Full Text: DOI
Ramani, A.; Grammaticos, B.; Tamizhmani, K. M.; Tamizhmani, T. Higher linearizable mappings and their explicit integration. (English) Zbl 1263.39010 J. Phys. A, Math. Theor. 46, No. 6, Article ID 065201, 17 p. (2013). MSC: 39A12 39A20 34M55 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 46, No. 6, Article ID 065201, 17 p. (2013; Zbl 1263.39010) Full Text: DOI
Mimura, N.; Isojima, S.; Murata, M.; Satsuma, J.; Ramani, A.; Grammaticos, B. Do ultradiscrete systems with parity variables satisfy the singularity confinement criterion? (English) Zbl 1274.37009 J. Math. Phys. 53, No. 2, 023510, 24 p. (2012). MSC: 37B15 39A12 37K10 37K40 PDFBibTeX XMLCite \textit{N. Mimura} et al., J. Math. Phys. 53, No. 2, 023510, 24 p. (2012; Zbl 1274.37009) Full Text: DOI
Ramani, A.; Grammaticos, B.; Satsuma, J. On the explicit integration of a class of linearizable mappings. (English) Zbl 1253.37068 J. Phys. A, Math. Theor. 45, No. 36, Article ID 365202, 13 p. (2012). Reviewer: Masataka Kanki (Tokyo) MSC: 37K10 39A12 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 45, No. 36, Article ID 365202, 13 p. (2012; Zbl 1253.37068) Full Text: DOI
Ramani, A.; Grammaticos, B.; Satsuma, J.; Mimura, N. Linearizable QRT mappings. (English) Zbl 1246.37090 J. Phys. A, Math. Theor. 44, No. 42, Article ID 425201, 18 p. (2011). MSC: 37K10 39A12 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 44, No. 42, Article ID 425201, 18 p. (2011; Zbl 1246.37090) Full Text: DOI
Grammaticos, Basil; Ramani, Alfred Painlevé equations: continuous, discrete and ultradiscrete. (English) Zbl 1229.39008 Levi, Decio (ed.) et al., Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Cambridge: Cambridge University Press (ISBN 978-0-521-13658-7/pbk). London Mathematical Society Lecture Note Series 381, 50-82 (2011). MSC: 39A12 34M55 37J05 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, Lond. Math. Soc. Lect. Note Ser. 381, 50--82 (2011; Zbl 1229.39008)
Grammaticos, B.; Ramani, A.; Willox, R. Folding transformations and HKY mappings. (English) Zbl 1218.39009 J. Nonlinear Math. Phys. 18, No. 1, 75-85 (2011). MSC: 39A20 39A12 37J15 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Nonlinear Math. Phys. 18, No. 1, 75--85 (2011; Zbl 1218.39009) Full Text: DOI
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
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M. Mappings of Hirota-Kimura-Yahagi type can have periodic coefficients too. (English) Zbl 1206.39007 J. Phys. A, Math. Theor. 44, No. 1, Article ID 015206, 11 p. (2011). MSC: 39A12 39A20 37J15 39A23 37J35 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Phys. A, Math. Theor. 44, No. 1, Article ID 015206, 11 p. (2011; Zbl 1206.39007) Full Text: DOI
Ramani, A.; Grammaticos, B.; Tamizhmani, K. M. From discrete Painlevé equations to mappings with periodic coefficients and back. (English) Zbl 1211.37072 J. Phys. A, Math. Theor. 43, No. 48, Article ID 485202, 10 p. (2010). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37J35 33E17 34M55 39A12 33E05 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 43, No. 48, Article ID 485202, 10 p. (2010; Zbl 1211.37072) Full Text: DOI
Willox, Ralph; Nakata, Yoichi; Satsuma, Junkichi; Ramani, Alfred; Grammaticos, Basile Solving the ultradiscrete KdV equation. (English) Zbl 1205.35281 J. Phys. A, Math. Theor. 43, No. 48, Article ID 482003, 7 p. (2010). MSC: 35Q53 39A12 35C08 PDFBibTeX XMLCite \textit{R. Willox} et al., J. Phys. A, Math. Theor. 43, No. 48, Article ID 482003, 7 p. (2010; Zbl 1205.35281) Full Text: DOI
Murata, M.; Satsuma, J.; Ramani, A.; Grammaticos, B. How to discretize differential systems in a systematic way. (English) Zbl 1222.39009 J. Phys. A, Math. Theor. 43, No. 31, Article ID 315203, 15 p. (2010). Reviewer: Alexander Odesskii (Thorold) MSC: 39A12 37K10 PDFBibTeX XMLCite \textit{M. Murata} et al., J. Phys. A, Math. Theor. 43, No. 31, Article ID 315203, 15 p. (2010; Zbl 1222.39009) Full Text: DOI
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
Grammaticos, Basil; Ramani, Alfred Singularity confinement property for the (non-autonomous) Adler-Bobenko-Suris integrable lattice equations. (English) Zbl 1190.37064 Lett. Math. Phys. 92, No. 1, 33-45 (2010). MSC: 37J35 39A12 37J15 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, Lett. Math. Phys. 92, No. 1, 33--45 (2010; Zbl 1190.37064) Full Text: DOI
Grammaticos, B.; Ramani, A.; Tamizhmani, T. Investigating the integrability of the Lyness mappings. (English) Zbl 1186.39008 J. Phys. A, Math. Theor. 42, No. 45, Article ID 454009, 7 p. (2009). Reviewer: Peter Zabreiko (Minsk) MSC: 39A20 39A12 37K10 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Phys. A, Math. Theor. 42, No. 45, Article ID 454009, 7 p. (2009; Zbl 1186.39008) Full Text: DOI
Ramani, A.; Grammaticos, B.; Satsuma, J.; Willox, R. On two (not so) new integrable partial difference equations. (English) Zbl 1172.35509 J. Phys. A, Math. Theor. 42, No. 28, Article ID 282002, 6 p., 6 p. (2009). MSC: 35R10 39A12 35Q53 35A30 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 42, No. 28, Article ID 282002, 6 p., 6 p. (2009; Zbl 1172.35509) Full Text: DOI
Joshi, N.; Lafortune, S.; Ramani, A. Hirota bilinear formalism and ultra-discrete singularity analysis. (English) Zbl 1172.39021 Nonlinearity 22, No. 4, 871-887 (2009). Reviewer: Hussain A. El-Saify (Beni Suef) MSC: 39A12 39A10 35Q53 37K10 37B15 PDFBibTeX XMLCite \textit{N. Joshi} et al., Nonlinearity 22, No. 4, 871--887 (2009; Zbl 1172.39021) Full Text: DOI Link
Ramani, A.; Nagoya, H.; Grammaticos, B.; Tamizhmani, T. Folding transformations for quantum Painlevé equations. (English) Zbl 1166.34335 J. Phys. A, Math. Theor. 42, No. 9, Article ID 095211, 9 p. (2009). MSC: 34M55 39A10 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Theor. 42, No. 9, Article ID 095211, 9 p. (2009; Zbl 1166.34335) Full Text: DOI
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)
Ramani, A.; Grammaticos, B.; Willox, R. Contiguity relations for discrete and ultradiscrete Painlevé equations. (English) Zbl 1163.39009 J. Nonlinear Math. Phys. 15, No. 4, 353-364 (2008). MSC: 39A12 34M55 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Nonlinear Math. Phys. 15, No. 4, 353--364 (2008; Zbl 1163.39009) Full Text: DOI
Nagoya, Hajime; Grammaticos, Basil; Ramani, Alfred Quantum Painlevé equations: from continuous to discrete. (English) Zbl 1154.34045 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 051, 9 p. (2008). Reviewer: Galina Filipuk (Warszawa) MSC: 34M55 39A10 PDFBibTeX XMLCite \textit{H. Nagoya} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 051, 9 p. (2008; Zbl 1154.34045) Full Text: DOI arXiv EuDML
Tsuda, Teruhisa; Grammaticos, Basil; Ramani, Alfred; Takenawa, Tomoyuki A class of integrable and nonintegrable mappings and their dynamics. (English) Zbl 1129.37032 Lett. Math. Phys. 82, No. 1, 39-49 (2007). MSC: 37J35 39A12 37J30 PDFBibTeX XMLCite \textit{T. Tsuda} et al., Lett. Math. Phys. 82, No. 1, 39--49 (2007; Zbl 1129.37032) Full Text: DOI
Ramani, Alfred; Grammaticos, Basil; Tamizhmani, Thamizharasi On the alternate discrete Painlevé equations and related systems. (English) Zbl 1137.39012 Delabaere, Éric (ed.) et al., Théories asymptotiques et équations de Painlevé. Paris: Société Mathématique de France (ISBN 978-2-85629-229-7/pbk). Séminaires et Congrès 14, 237-247 (2006). MSC: 39A12 34M55 PDFBibTeX XMLCite \textit{A. Ramani} et al., Sémin. Congr. 14, 237--247 (2006; Zbl 1137.39012)
Grammaticos, B.; Ramani, A.; Takenawa, T. On the identity of two \(q\)-discrete Painlevé equations and their geometrical derivation. (English) Zbl 1140.39313 Adv. Difference Equ. 2006, Article ID 36397, 11 p. (2006). MSC: 39A12 34M55 39A13 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., Adv. Difference Equ. 2006, Article ID 36397, 11 p. (2006; Zbl 1140.39313) Full Text: DOI EuDML
Grammaticos, B.; Ramani, A.; Carstea, A. S. Bilinear avatars of the discrete Painlevé II equation. (English) Zbl 1126.39015 Faddeev, Ludwig (ed.) et al., Bilinear integrable systems. From classical to quantum, continuous to discrete. Proceedings of the NATO advanced research workshop, St. Petersburg, Russia, September 15–19, 2002. Dordrecht: Springer (ISBN 978-1-4020-3502-9/pbk; 978-1-4020-3501-2/hbk; 978-1-4020-3503-6/e-book). NATO Science Series II: Mathematics, Physics and Chemistry 201, 85-96 (2006). MSC: 39A13 39A12 34M55 39A20 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., NATO Sci. Ser. II, Math. Phys. Chem. 201, 85--96 (2006; Zbl 1126.39015) Full Text: DOI
Ramani, A.; Ohta, Y.; Grammaticos, B. Discrete systems related to the sixth Painlevé equation. (English) Zbl 1108.39016 J. Phys. A, Math. Gen. 39, No. 39, 12167-12178 (2006). MSC: 39A12 34M55 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 39, No. 39, 12167--12178 (2006; Zbl 1108.39016) Full Text: DOI
Joshi, N.; Grammaticos, B.; Tamizhmani, T.; Ramani, A. From integrable lattices to non-QRT mappings. (English) Zbl 1111.39013 Lett. Math. Phys. 78, No. 1, 27-37 (2006). Reviewer: Edwin Engin Yaz (Milwaukee) MSC: 39A12 37J15 37J35 PDFBibTeX XMLCite \textit{N. Joshi} et al., Lett. Math. Phys. 78, No. 1, 27--37 (2006; Zbl 1111.39013) 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
Ramani, A.; Grammaticos, B. On the discrete form of the Fokas–Ablowitz equation. (English) Zbl 1089.39006 Chaos Solitons Fractals 24, No. 5, 1331-1335 (2005). Reviewer: Alberto Cabada (Santiago de Compostela) MSC: 39A13 37K10 39A12 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, Chaos Solitons Fractals 24, No. 5, 1331--1335 (2005; Zbl 1089.39006) Full Text: DOI
Tamizhmani, K. M.; Ramani, A.; Grammaticos, B.; Carstea, A. S. Modelling AIDS epidemic and treatment with difference equations. (English) Zbl 1068.92030 Adv. Difference Equ. 2004, No. 3, 183-193 (2004). MSC: 92C50 93A30 39A10 92C60 39A13 PDFBibTeX XMLCite \textit{K. M. Tamizhmani} et al., Adv. Difference Equ. 2004, No. 3, 183--193 (2004; Zbl 1068.92030) Full Text: DOI EuDML
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)
Grammaticos, B.; Ramani, A. Discrete Painlevé equations: a review. (English) Zbl 1064.39019 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, 245-321 (2004). MSC: 39A12 39-02 34M55 33E17 37J35 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, Lect. Notes Phys. 644, 245--321 (2004; Zbl 1064.39019)
Tamizhmani, K. M.; Grammaticos, B.; Carstea, A. S.; Ramani, A. The \(q\)-discrete Painlevé IV equations and their properties. (English) Zbl 1053.39034 Regul. Chaotic Dyn. 9, No. 1, 13-20 (2004). Reviewer: A. E. Mironov (Novosibirsk) MSC: 39A13 39A12 34M55 PDFBibTeX XMLCite \textit{K. M. Tamizhmani} et al., Regul. Chaotic Dyn. 9, No. 1, 13--20 (2004; Zbl 1053.39034)
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M. The road to the discrete analogue of the Painlevé property: Nevanlinna meets singularity confinement. (English) Zbl 1057.39018 Comput. Math. Appl. 45, No. 6-9, 1001-1012 (2003). Reviewer: D. M. Bors (Iaşi) MSC: 39A12 30D35 34M55 37J35 PDFBibTeX XMLCite \textit{A. Ramani} et al., Comput. Math. Appl. 45, No. 6--9, 1001--1012 (2003; Zbl 1057.39018) Full Text: DOI
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
Tamizhmani, K. M.; Ramani, A.; Tamizhmani, T.; Grammaticos, B. Special functions as solutions to discrete Painlevé equations. (English) Zbl 1107.39303 J. Comput. Appl. Math. 160, No. 1-2, 307-313 (2003). MSC: 39A12 33E17 34M55 37J35 PDFBibTeX XMLCite \textit{K. M. Tamizhmani} et al., J. Comput. Appl. Math. 160, No. 1--2, 307--313 (2003; Zbl 1107.39303) Full Text: DOI
Takenawa, T.; Eguchi, M.; Grammaticos, B.; Ohta, Y.; Ramani, A.; Satsuma, J. The space of initial conditions for linearizable mappings. (English) Zbl 1021.37023 Nonlinearity 16, No. 2, 457-477 (2003). MSC: 37F10 37F50 39A12 PDFBibTeX XMLCite \textit{T. Takenawa} et al., Nonlinearity 16, No. 2, 457--477 (2003; Zbl 1021.37023) Full Text: DOI arXiv
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
Tamizhmani, T.; Grammaticos, B.; Ramani, A.; Tamizhmani, K. M. A Nevanlinna theory approach to the integrability of discrete systems. (English) Zbl 1056.39026 Sahadevan, R. (ed.) et al., Nonlinear systems. Proceedings of the 8th Ramanujan symposium on recent developments in nonlinear systems, University of Madras, Chennai, India, February 14–16, 2001. Boca Raton, FL: Chapman and Hall/CRC; New Delhi: Narosa Publishing House (ISBN 0-8493-1722-3; 81-7319-456-4). 297-305 (2002). MSC: 39A12 30D35 37J10 PDFBibTeX XMLCite \textit{T. Tamizhmani} et al., in: Nonlinear systems. Proceedings of the 8th Ramanujan symposium on recent developments in nonlinear systems, University of Madras, Chennai, India, February 14--16, 2001. Boca Raton, FL: Chapman and Hall/CRC; New Delhi: Narosa Publishing House. 297--305 (2002; Zbl 1056.39026)
Tamizhmani, K. M.; Grammaticos, B.; Tamizhmani, T.; Ramani, A. A panorama of the special solutions of the Painlevé equations. (English) Zbl 1057.39019 Sahadevan, R. (ed.) et al., Nonlinear systems. Proceedings of the 8th Ramanujan symposium on recent developments in nonlinear systems, University of Madras, Chennai, India, February 14–16, 2001. Boca Raton, FL: Chapman and Hall/CRC; New Delhi: Narosa Publishing House (ISBN 0-8493-1722-3; 81-7319-456-4). 265-280 (2002). MSC: 39A12 34M55 33E17 PDFBibTeX XMLCite \textit{K. M. Tamizhmani} et al., in: Nonlinear systems. Proceedings of the 8th Ramanujan symposium on recent developments in nonlinear systems, University of Madras, Chennai, India, February 14--16, 2001. Boca Raton, FL: Chapman and Hall/CRC; New Delhi: Narosa Publishing House. 265--280 (2002; Zbl 1057.39019)
Kimura, K.; Yahagi, H.; Hirota, R.; Ramani, A.; Grammaticos, B.; Ohta, Y. A new class of integrable discrete systems. (English) Zbl 1042.37012 J. Phys. A, Math. Gen. 35, No. 43, 9205-9212 (2002). MSC: 37C05 33E05 33E17 34M55 39A13 PDFBibTeX XMLCite \textit{K. Kimura} et al., J. Phys. A, Math. Gen. 35, No. 43, 9205--9212 (2002; Zbl 1042.37012) Full Text: DOI
Ohta, Y.; Ramani, A.; Grammaticos, B. Elliptic discrete Painlevé equations. (English) Zbl 1056.39027 J. Phys. A, Math. Gen. 35, No. 45, L653-L659 (2002). Reviewer: Jacques Sauloy (Toulouse) MSC: 39A13 39A12 39A70 34M55 PDFBibTeX XMLCite \textit{Y. Ohta} et al., J. Phys. A, Math. Gen. 35, No. 45, L653--L659 (2002; Zbl 1056.39027) Full Text: DOI
Ramani, A.; Grammaticos, B.; Lafortune, S. The discrete Chazy III system of Labrunie-Conte is not integrable. (English) Zbl 1046.39012 J. Phys. A, Math. Gen. 35, No. 37, 7943-7946 (2002). Reviewer: Marat Akhmet (Ankara) MSC: 39A12 37J30 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 35, No. 37, 7943--7946 (2002; Zbl 1046.39012) 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
Ramani, A.; Grammaticos, B. What is the discrete analogue of the Painlevé property? (English) Zbl 1014.39014 ANZIAM J. 44, No. 1, 21-32 (2002). Reviewer: S.Balint (Timişoara) MSC: 39A12 37J35 34M55 PDFBibTeX XMLCite \textit{A. Ramani} and \textit{B. Grammaticos}, ANZIAM J. 44, No. 1, 21--32 (2002; Zbl 1014.39014) Full Text: DOI
Ramani, A.; Carstea, A. S.; Grammaticos, B.; Ohta, Y. On the autonomous limit of discrete Painlevé equations. (English) Zbl 0992.39015 Physica A 305, No. 3-4, 437-444 (2002). MSC: 39A12 34M55 PDFBibTeX XMLCite \textit{A. Ramani} et al., Physica A 305, No. 3--4, 437--444 (2002; Zbl 0992.39015) Full Text: DOI
Lafortune, S.; Carstea, A. S.; Ramani, A.; Grammaticos, B.; Ohta, Y. Integrable third-order mappings and their growth properties. (English) Zbl 1011.39017 Regul. Chaotic Dyn. 6, No. 4, 443-448 (2001). Reviewer: I.A.Taimanov (Novosibirsk) MSC: 39A12 34M55 37J35 PDFBibTeX XMLCite \textit{S. Lafortune} et al., Regul. Chaotic Dyn. 6, No. 4, 443--448 (2001; Zbl 1011.39017)
Nijhoff, F. W.; Ramani, A.; Grammaticos, B.; Ohta, Y. On discrete Painlevé equations associated with the lattice KdV systems and the Painlevé VI equation. (English) Zbl 1152.39313 Stud. Appl. Math. 106, No. 3, 261-314 (2001). MSC: 39A12 34M55 37K60 PDFBibTeX XMLCite \textit{F. W. Nijhoff} et al., Stud. Appl. Math. 106, No. 3, 261--314 (2001; Zbl 1152.39313) 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
Ramani, A.; Grammaticos, B.; Tamizhmani, T.; Tamizhmani, K. M. Special function solutions of the discrete Painlevé equations. (English) Zbl 0994.33500 Comput. Math. Appl. 42, No. 3-5, 603-614 (2001). Reviewer: J.Saurer (Regensburg) MSC: 33E17 39A12 65Q05 PDFBibTeX XMLCite \textit{A. Ramani} et al., Comput. Math. Appl. 42, No. 3--5, 603--614 (2001; Zbl 0994.33500) Full Text: DOI
Ohta, Yasuhiro; Ramani, A.; Grammaticos, B. An affine Weyl group approach to the 8-parameter discrete Painlevé equation. (English) Zbl 0985.39500 RIMS Kokyuroku 1203, 109-119 (2001). MSC: 39A12 37K35 PDFBibTeX XMLCite \textit{Y. Ohta} et al., RIMS Kokyuroku 1203, 109--119 (2001; Zbl 0985.39500)
Lafortune, S.; Ramani, A.; Grammaticos, B.; Ohta, Y.; Tamizhmani, K. M. Blending two discrete integrability criteria: Singularity confinement and algebraic entropy. (English) Zbl 0991.39009 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, 299-311 (2001). MSC: 39A12 39B05 37J35 PDFBibTeX XMLCite \textit{S. Lafortune} 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). 299--311 (2001; Zbl 0991.39009) Full Text: arXiv
Ohta, Y.; Ramani, A.; Grammaticos, B. An affine Weyl group approach to the eight-parameter discrete Painlevé equation. (English) Zbl 1002.39029 J. Phys. A, Math. Gen. 34, No. 48, 10523-10532 (2001). MSC: 39A12 39A13 34M55 PDFBibTeX XMLCite \textit{Y. Ohta} et al., J. Phys. A, Math. Gen. 34, No. 48, 10523--10532 (2001; Zbl 1002.39029) Full Text: DOI
Ramani, A.; Grammaticos, B.; Ohta, Y. A geometrical description of the discrete Painlevé VI and V equations. (English) Zbl 0980.39010 Commun. Math. Phys. 217, No. 2, 315-329 (2001). Reviewer: Pavel Talpalaru (Iaşi) MSC: 39A13 39A12 37J99 34M55 17B80 PDFBibTeX XMLCite \textit{A. Ramani} et al., Commun. Math. Phys. 217, No. 2, 315--329 (2001; Zbl 0980.39010) Full Text: DOI
Ramani, A.; Grammaticos, B.; Ohta, Y. The \(q\)-Painlevé V equation and its geometrical description. (English) Zbl 0980.39009 J. Phys. A, Math. Gen. 34, No. 11, 2505-2513 (2001). Reviewer: Pavel Talpalaru (Iaşi) MSC: 39A13 39A12 34M55 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 34, No. 11, 2505--2513 (2001; Zbl 0980.39009) Full Text: DOI
Lafortune, S.; Grammaticos, B.; Ramani, A.; Winternitz, P. Discrete systems related to some equations of the Painlevé-Gambier classification. (English) Zbl 1115.39302 Phys. Lett., A 270, No. 1-2, 55-61 (2000). MSC: 39A12 34A34 37K10 PDFBibTeX XMLCite \textit{S. Lafortune} et al., Phys. Lett., A 270, No. 1--2, 55--61 (2000; Zbl 1115.39302) 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
Ramani, A.; Grammaticos, B.; Tamizhmani, T. Special relations for continuous and discrete Painlevé equations. (English) Zbl 0998.33012 J. Phys. A, Math. Gen. 33, No. 44, L415-L421 (2000). MSC: 33E17 34M55 39A12 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 33, No. 44, L415--L421 (2000; Zbl 0998.33012) Full Text: DOI
Ramani, A.; Grammaticos, B.; Lafortune, S.; Ohta, Y. Linearizable mappings and the low-growth criterion. (English) Zbl 0962.37020 J. Phys. A, Math. Gen. 33, No. 31, L287-L292 (2000). MSC: 37E30 39A12 37C15 37K10 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 33, No. 31, L287--L292 (2000; Zbl 0962.37020) Full Text: DOI arXiv
Ramani, A.; Grammaticos, B.; Lafortune, S. A study of the continuous and discrete Gambier systems. (English) Zbl 0959.39020 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, 367-380 (2000). MSC: 39A12 37J35 PDFBibTeX XMLCite \textit{A. Ramani} 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). 367--380 (2000; Zbl 0959.39020) Full Text: arXiv
Lafortune, S.; Grammaticos, B.; Ramani, A. Linearisable systems and the Gambier approach. (English) Zbl 0959.39019 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, 255-261 (2000). MSC: 39A12 34A34 37J35 34M55 PDFBibTeX XMLCite \textit{S. Lafortune} 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). 255--261 (2000; Zbl 0959.39019) Full Text: arXiv
Ramani, A.; Grammaticos, B.; Tamizhmani, T. Quadratic relations in continuous and discrete Painlevé equations. (English) Zbl 0953.34078 J. Phys. A, Math. Gen. 33, No. 15, 3033-3044 (2000). MSC: 34M55 39A13 34A34 39A12 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 33, No. 15, 3033--3044 (2000; Zbl 0953.34078) Full Text: DOI
Ramani, A.; Grammaticos, B.; Tremblay, S. Integrable systems without the Painlevé property. (English) Zbl 0953.34077 J. Phys. A, Math. Gen. 33, No. 15, 3045-3052 (2000). MSC: 34M55 39A12 34A34 37J35 PDFBibTeX XMLCite \textit{A. Ramani} et al., J. Phys. A, Math. Gen. 33, No. 15, 3045--3052 (2000; Zbl 0953.34077) Full Text: DOI 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. The hunting for the discrete Painlevé equations. (English) Zbl 0951.39005 Regul. Chaotic Dyn. 5, No. 1, 53-66 (2000). Reviewer: I.A.Taimanov (Novosibirsk) MSC: 39A12 37J35 34M55 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, Regul. Chaotic Dyn. 5, No. 1, 53--66 (2000; Zbl 0951.39005)
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
Grammaticos, Basile; Nijhoff, Frank W.; Ramani, Alfred Discrete Painlevé equations. (English) Zbl 1014.39013 Conte, Robert (ed.), The Painlevé property. One century later. New York, NY: Springer. CRM Series in Mathematical Physics. 413-516 (1999). MSC: 39A12 37J35 34M55 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., in: The Painlevé property. One century later. New York, NY: Springer. 413--516 (1999; Zbl 1014.39013)
Tamizhmani, T.; Tamizhmani, K. M.; Grammaticos, B.; Ramani, A. Special function solutions for asymmetric discrete Painlevé equations. (English) Zbl 0944.39004 J. Phys. A, Math. Gen. 32, No. 24, 4553-4562 (1999). Reviewer: Th.M.Rassias (Athens) MSC: 39A12 33C05 33D15 PDFBibTeX XMLCite \textit{T. Tamizhmani} et al., J. Phys. A, Math. Gen. 32, No. 24, 4553--4562 (1999; Zbl 0944.39004) Full Text: DOI
Grammaticos, B.; Ramani, A. On a novel \(q\)-discrete analogue of the Painlevé VI equation. (English) Zbl 0938.39020 Phys. Lett., A 257, No. 5-6, 288-292 (1999). MSC: 39A13 33D15 PDFBibTeX XMLCite \textit{B. Grammaticos} and \textit{A. Ramani}, Phys. Lett., A 257, No. 5--6, 288--292 (1999; Zbl 0938.39020) Full Text: DOI
Grammaticos, B.; Ramani, A.; Winternitz, P. Discretizing families of linearizable equations. (English) Zbl 1044.37529 Phys. Lett., A 245, No. 5, 382-388 (1998). MSC: 37K10 39A12 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., Phys. Lett., A 245, No. 5, 382--388 (1998; Zbl 1044.37529) Full Text: DOI
Ramani, A.; Takahashi, D.; Grammaticos, B.; Ohta, Y. The ultimate discretisation of the Painlevé equations. (English) Zbl 0936.39006 Physica D 114, No. 3-4, 185-196 (1998). MSC: 39A12 37K35 PDFBibTeX XMLCite \textit{A. Ramani} et al., Physica D 114, No. 3--4, 185--196 (1998; Zbl 0936.39006) Full Text: DOI