RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (507 kB)
First page: PDF file
References: PDF file   HTML file

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
\Bibitem{GubLevSci16} \by G.~Gubbiotti, D.~Levi, Ch.~Scimiterna \paper Linearizability and a~fake Lax pair for a~nonlinear nonautonomous quad-graph equation consistent around the~cube \jour TMF \yr 2016 \vol 189 \issue 1 \pages 69--83 \mathnet{http://mi.mathnet.ru/tmf9079} \crossref{https://doi.org/10.4213/tmf9079} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3589022} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016TMP...189.1459G} \elib{http://elibrary.ru/item.asp?id=27350122} \transl \jour Theoret. and Math. Phys. \yr 2016 \vol 189 \issue 1 \pages 1459--1471 \crossref{https://doi.org/10.1134/S0040577916100068} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000386870200006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85013950480} 

• http://mi.mathnet.ru/eng/tmf9079
• https://doi.org/10.4213/tmf9079
• http://mi.mathnet.ru/eng/tmf/v189/i1/p69

 SHARE:

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

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
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
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
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
5. Ch. Scimiterna, G. Gubbiotti, “Reconstructing a lattice equation: a non-autonomous approach to the Hietarinta equation”, SIGMA, 14 (2018), 004, 21 pp.
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.
•  Number of views: This page: 135 References: 21 First page: 11