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TMF, 2016, Volume 189, Number 1, Pages 69–83 (Mi tmf9079)  

This article is cited in 6 scientific papers (total in 6 papers)

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

G. Gubbiottiab, D. Leviab, Ch. Scimiternaab

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

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, $C$-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").


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

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English version:
Theoretical and Mathematical Physics, 2016, 189:1, 1459–1471

Bibliographic databases:

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

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Grundland, D. Levi, L. Martina, “On immersion formulas for soliton surfaces”, Acta Polytech., 56:3 (2016), 180–192  crossref  isi  scopus
    2. 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  crossref  isi  scopus
    3. G. Gubbiotti, C. Scimiterna, D. Levi, “The non-autonomous YdKN equation and generalized symmetries of Boll equations”, J. Math. Phys., 58:5 (2017), 053507  crossref  mathscinet  zmath  isi  scopus
    4. 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  crossref  mathscinet  isi  scopus
    5. Ch. Scimiterna, G. Gubbiotti, “Reconstructing a lattice equation: a non-autonomous approach to the Hietarinta equation”, SIGMA, 14 (2018), 004, 21 pp.  mathnet  crossref
    6. R. I. Yamilov, Ch. Scimiterna, G. Gubbiotti, “Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions”, SIGMA, 14 (2018), 008, 51 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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