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
Nakazono, Nobutaka Discrete Painlevé transcendent solutions to the multiplicative-type discrete KdV equations. (English) Zbl 1507.39001 J. Math. Phys. 63, No. 4, Article ID 042703, 17 p. (2022). MSC: 39A12 39A13 39A36 34M55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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
Cao, Tingbin; Xu, Ling Logarithmic difference lemma in several complex variables and partial difference equations. (English) Zbl 1436.39009 Ann. Mat. Pura Appl. (4) 199, No. 2, 767-794 (2020). Reviewer: Eszter Gselmann (Debrecen) MSC: 39A14 39A45 32A22 32A20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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
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
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
Folly-Gbetoula, Mensah K.; Kara, Abdul H. Symmetries, conservation laws, and ‘integrability’ of difference equations. (English) Zbl 1417.39012 Adv. Difference Equ. 2014, Paper No. 224, 14 p. (2014). MSC: 39A12 34C14 × Cite Format Result Cite Review PDF Full Text: DOI OA License
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
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
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
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