Gubbiotti, Giorgio Algebraic entropy for systems of quad equations. (English) Zbl 07915241 Open Commun. Nonlinear Math. Phys. 2024, Spec. Iss. 1, Paper No. 17, 24 p. (2024). MSC: 37-XX × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Hietarinta, Jarmo Degree growth of lattice equations defined on a \(3\times 3\) stencil. (English) Zbl 07915237 Open Commun. Nonlinear Math. Phys. 2024, Spec. Iss. 1, Paper No. 13, 19 p. (2024). MSC: 37-XX 35-XX × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Nakazono, Nobutaka Consistency around a cube property of Hirota’s discrete KdV equation and the lattice sine-Gordon equation. (English) Zbl 07856328 Appl. Numer. Math. 199, 136-152 (2024). MSC: 39A36 39A14 37K60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Grammaticos, Basil; Willox, Ralph Full-deautonomisation of a class of second-order mappings in ancillary form. (English) Zbl 07888204 Open Commun. Nonlinear Math. Phys. 3, 1-22 (2023). MSC: 37J70 37J37 39A36 × Cite Format Result Cite Review PDF Full Text: DOI
Koumantos, Panagiotis N. On the mean ergodic theorem in bicomplex Banach modules. (English) Zbl 07650809 Adv. Appl. Clifford Algebr. 33, No. 1, Paper No. 14, 19 p. (2023). MSC: 47A35 37A30 46A19 30G35 × Cite Format Result Cite Review PDF Full Text: DOI
Nakazono, Nobutaka Properties of the non-autonomous lattice sine-Gordon equation: consistency around a broken cube property. (English) Zbl 1497.37092 SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 032, 8 p. (2022). MSC: 37K60 39A36 39A14 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gubbiotti, Giorgio; Kels, Andrew P. Algebraic entropy for face-centered quad equations. (English) Zbl 1519.37097 J. Phys. A, Math. Theor. 54, No. 45, Article ID 455201, 44 p. (2021). MSC: 37K60 39A14 39A36 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Joshi, Nalini; Nakazono, Nobutaka On the three-dimensional consistency of Hirota’s discrete Korteweg-de Vries equation. (English) Zbl 1483.39009 Stud. Appl. Math. 147, No. 4, 1409-1424 (2021). MSC: 39A36 37K60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Demskoi, Dmitry K. The lattice sine-Gordon equation as a superposition formula for an NLS-type system. (English) Zbl 1483.35176 SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 108, 10 p. (2021). MSC: 35Q51 35Q55 37K60 37K10 35C08 37K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Viallet, Claude M. Features of discrete integrability. (English) Zbl 1479.39022 Paranjape, M. B. (ed.) et al., Quantum theory and symmetries. Proceedings of the 11th international symposium, Montréal, Canada, July 1–5, 2019. Cham: Springer. CRM Ser. Math. Phys., 21-35 (2021). Reviewer: Pieter Roffelsen (Melbourne) MSC: 39A36 37J70 37K60 × Cite Format Result Cite Review PDF Full Text: DOI
Grammaticos, Basil; Ramani, Alfred Gambier lattices and other linearisable systems. (English) Zbl 1441.37084 J. Nonlinear Math. Phys. 27, No. 4, 688-696 (2020). MSC: 37K60 × Cite Format Result Cite Review PDF Full Text: DOI
Hietarinta, J.; Mase, T.; Willox, R. Algebraic entropy computations for lattice equations: why initial value problems do matter. (English) Zbl 1509.39013 J. Phys. A, Math. Theor. 52, No. 49, Article ID 49LT01, 13 p. (2019). MSC: 39A36 37K60 37J70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tran, Dinh T.; Roberts, John A. G. Linear degree growth in lattice equations. (English) Zbl 1478.37078 J. Comput. Dyn. 6, No. 2, 449-467 (2019). Reviewer: Giorgio Gubbiotti (Milano) MSC: 37K60 39A36 39A14 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gubbiotti, Giorgio Algebraic entropy of a class of five-point differential-difference equations. (English) Zbl 1423.34021 Symmetry 11, No. 3, Paper No. 432, 24 p. (2019). MSC: 34A33 34C14 37J35 39A12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Garifullin, Rustem N.; Gubbiotti, Giorgio; Yamilov, Ravil I. Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations. (English) Zbl 1417.37263 J. Nonlinear Math. Phys. 26, No. 3, 333-357 (2019). MSC: 37L20 37K10 39A14 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Roberts, John A. G.; Tran, Dinh T. Algebraic entropy of (integrable) lattice equations and their reductions. (English) Zbl 1410.39016 Nonlinearity 32, No. 2, 622-653 (2019). MSC: 39A14 37K10 65Q10 28D20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gubbiotti, Giorgio; Scimiterna, Christian Reconstructing a lattice equation: a non-autonomous approach to the Hietarinta equation. (English) Zbl 1387.37062 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 004, 21 p. (2018). Reviewer: Eszter Gselmann (Debrecen) MSC: 37K10 37K35 39A14 39A22 37K60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Peng, Linyu Symmetries, conservation laws, and Noether’s theorem for differential-difference equations. (English) Zbl 1386.37064 Stud. Appl. Math. 139, No. 3, 457-502 (2017). Reviewer: Ti-Jun Xiao (Fudan) MSC: 37K05 35L65 39A12 35A30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Benson, Joseph; Valiquette, Francis Symmetry reduction of ordinary finite difference equations using moving frames. (English) Zbl 1366.39001 J. Phys. A, Math. Theor. 50, No. 19, Article ID 195201, 24 p. (2017). MSC: 39A10 65Q30 37J15 × Cite Format Result Cite Review PDF Full Text: DOI
Gubbiotti, G.; Scimiterna, C.; Levi, D. Algebraic entropy, symmetries and linearization of quad equations consistent on the cube. (English) Zbl 1420.37064 J. Nonlinear Math. Phys. 23, No. 4, 507-543 (2016). MSC: 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gubbiotti, G.; Scimiterna, C.; Levi, Decio Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube. (English. Russian original) Zbl 1359.37132 Theor. Math. Phys. 189, No. 1, 1459-1471 (2016); translation from Teor. Mat. Fiz. 189, No. 1, 69-83 (2016). Reviewer: Eszter Gselmann (Debrecen) MSC: 37K10 37K35 39A14 × Cite Format Result Cite Review PDF Full Text: DOI
Sahadevan, R.; Nagavigneshwari, G. Continuous symmetries of certain nonlinear partial difference equations and their reductions. (English) Zbl 1343.39024 Phys. Lett., A 378, No. 43, 3155-3160 (2014). MSC: 39A14 37K10 37K05 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Wenlei; Shi, Shaoyun Weak-Painlevé property and integrability of general dynamical systems. (English) Zbl 1396.34055 Discrete Contin. Dyn. Syst. 34, No. 9, 3667-3681 (2014). MSC: 34M55 37K10 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Levi, Decio; Ricca, Eugenio; Thomova, Zora; Winternitz, Pavel Lie group analysis of a generalized Krichever-Novikov differential-difference equation. (English) Zbl 1366.39015 J. Math. Phys. 55, No. 10, 103503, 12 p. (2014). MSC: 39A70 37G99 17B80 34A33 34C14 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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 × Cite Format Result Cite Review PDF Full Text: DOI
van der Kamp, Peter H. Growth of degrees of integrable mappings. (English) Zbl 1238.39003 J. Difference Equ. Appl. 18, No. 3, 447-460 (2012). MSC: 39A12 35Q53 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hydon, Peter E.; Viallet, Claude-M. Asymmetric integrable quad-graph equations. (English) Zbl 1188.37059 Appl. Anal. 89, No. 4, 493-506 (2010). MSC: 37K10 39A12 37K05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Kravchenko, Viktor G.; Kravchenko, Vladislav V.; Tremblay, Sébastien Zakharov-Shabat system and hyperbolic pseudoanalytic function theory. (English) Zbl 1196.30043 Math. Methods Appl. Sci. 33, No. 4, 448-453 (2010). Reviewer: George Csordas (Honolulu) MSC: 30G20 37K15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sahadevan, R.; Maheswari, C. Uma Polynomial integrals for third- and fourth-order ordinary difference equations. (English) Zbl 1163.39010 J. Nonlinear Math. Phys. 15, No. 3, 299-315 (2008). MSC: 39A12 37K10 × Cite Format Result Cite Review PDF Full Text: DOI Link OA License
Viallet, C.-M. Algebraic dynamics and algebraic entropy. (English) Zbl 1198.37016 Int. J. Geom. Methods Mod. Phys. 5, No. 8, 1373-1391 (2008). MSC: 37A35 × Cite Format Result Cite Review PDF Full Text: DOI
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Carstea, A. S. Do all integrable equations satisfy integrability criteria? (English) Zbl 1145.37030 Adv. Difference Equ. 2008, Article ID 317520, 16 p. (2008). MSC: 37J35 37J30 × Cite Format Result Cite Review PDF Full Text: DOI EuDML OA License
Sahadevan, R.; Maheswari, C. Uma Direct method to construct integrals for \(N\)th-order autonomous ordinary difference equations. (English) Zbl 1141.37025 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 464, No. 2090, 341-364 (2008). MSC: 37K10 39A12 × Cite Format Result Cite Review PDF Full Text: DOI
Güngör, F.; Lahno, V. I.; Zhdanov, R. Z. Symmetry classification of KdV-type nonlinear evolution equations. (English) Zbl 1071.35112 J. Math. Phys. 45, No. 6, 2280-2313 (2004). MSC: 35Q53 35A30 37K05 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hu, Xing-Biao; Zhao, Jun-Xiao; Tam, Hon-Wah Pfaffianization of the two-dimensional Toda lattice. (English) Zbl 1051.37037 J. Math. Anal. Appl. 296, No. 1, 256-261 (2004). Reviewer: Ma Wen-Xiu (Tampa) MSC: 37K10 35Q51 37K60 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
Dorodonitsyn, Vladimir; Kozlov, Roman A heat transfer with a source: The complete set of invariant difference schemes. (English) Zbl 1026.65072 J. Nonlinear Math. Phys. 10, No. 1, 16-50 (2003). MSC: 65M06 35K55 22E15 37K60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Sakovich, S. Yu. On integrability of differential constraints arising form the singularity analysis. (English) Zbl 0991.35072 J. Nonlinear Math. Phys. 9, No. 1, 21-25 (2002). MSC: 35Q51 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License