G. Gubbiotti, D. Levi, Ch. Scimiterna, “Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube”, TMF, 189:1 (2016), 69–83; Theoret. and Math. Phys., 189:1 (2016), 1459

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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 1, Pages 69–83
DOI: https://doi.org/10.4213/tmf9079 (Mi tmf9079)

This article is cited in 11 scientific papers (total in 11 papers)

Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube

G. Gubbiotti^ab, D. Levi^ab, Ch. Scimiterna^ab

^a Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Roma, Italy
^b Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Roma, Italy

Full-text PDF (507 kB) Citations (11)

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DOI: https://doi.org/10.4213/tmf9079

Abstract: We discuss the linearization of a nonautonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized symmetries, which turn out to be nonautonomous and dependent on an arbitrary function of the dependent variables defined at two lattice points. The se generalized symmetries are differential–difference equations, which admit peculiar Bäcklund transformations in some cases.

Keywords: partial difference equation,

C

$C$ -integrability, Bäcklund transformation, fake Lax pair.

Funding agency	Grant number
Italian Ministry of Education, University and Research
Instituto Nazionale di Fisica Nucleare	IS-CSN4
The research of G. Gubbiotti was supported by INFN IS-CSN4 "Mathematical Methods of Nonlinear Physics. The research of C. Scimiterna was supported in part by the Italian Ministry of Education and Research (2010 PRIN "Continuous and discrete nonlinear integrable evolutions: From water waves to symplectic maps"). The research of D. Levi was supported by INFN IS-CSN4 "Mathematical Methods of Nonlinear Physics" and in part by the Italian Ministry of Education and Research (2010 PRIN "Continuous and discrete nonlinear integrable evolutions: From water waves to symplectic maps").

English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 1, Pages 1459–1471
DOI: https://doi.org/10.1134/S0040577916100068

Bibliographic databases:

MSC: 39AXX, 70G65, 39A06,37K10

Language: Russian

Citation: G. Gubbiotti, D. Levi, Ch. Scimiterna, “Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube”, TMF, 189:1 (2016), 69–83; Theoret. and Math. Phys., 189:1 (2016), 1459–1471

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Linking options:

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https://doi.org/10.4213/tmf9079

https://www.mathnet.ru/eng/tmf/v189/i1/p69

This publication is cited in the following 11 articles:

Giorgio Gubbiotti, “Algebraic entropy for systems of quad equations”, Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of... (2024)
Giorgio Gubbiotti, Andrew P Kels, Claude-M Viallet, “Algebraic entropy for hex systems”, Nonlinearity, 37:12 (2024), 125007
G. Gubbiotti, A. P. Kels, “Algebraic entropy for face-centered quad equations”, J. Phys. A-Math. Theor., 54:45 (2021), 455201
Giorgio Gubbiotti, Nalini Joshi, Dinh Thi Tran, Claude-Michel Viallet, Springer Proceedings in Mathematics & Statistics, 338, Asymptotic, Algebraic and Geometric Aspects of Integrable Systems, 2020, 17
Giorgio Gubbiotti, Christian Scimiterna, “Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation”, SIGMA, 14 (2018), 004, 21 pp.
Giorgio Gubbiotti, Christian Scimiterna, Ravil I. Yamilov, “Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions”, SIGMA, 14 (2018), 008, 51 pp.
G. Gubbiotti, C. Scimiterna, D. Levi, “The non-autonomous YdKN equation and generalized symmetries of Boll equations”, J. Math. Phys., 58:5 (2017), 053507
G. Gubbiotti, R. I. Yamilov, “Darboux integrability of trapezoidal $H^{4}$ and $H^{6}$ families of lattice equations I: first integrals”, J. Phys. A-Math. Theor., 50:34 (2017), 345205, 1–26
Gubbiotti G., “Integrability of Difference Equations Through Algebraic Entropy and Generalized Symmetries”, Symmetries and Integrability of Difference Equations, Crm Series in Mathematical Physics, ed. Levi D. Rebelo R. Winternitz P., Springer, 2017, 75–151
A. M. Grundland, D. Levi, L. Martina, “On immersion formulas for soliton surfaces”, Acta Polytech., 56:3 (2016), 180–192
G. Gubbiotti, D. Levi, Ch. Scimiterna, “On partial differential and difference equations with symmetries depending on arbitrary functions”, Acta Polytech., 56:3 (2016), 193–201

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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