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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 10 scientific papers (total in 10 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
Full-text PDF (507 kB) Citations (10)
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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, $C$-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
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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