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SIGMA, 2018, Volume 14, 008, 51 pages (Mi sigma1307)  

This article is cited in 2 scientific papers (total in 2 papers)

Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions

Giorgio Gubbiottiabc, Christian Scimiternabc, Ravil I. Yamilovd

a School of Mathematics and Statistics, F07, The University of Sydney, New South Wales 2006, Australia
b Sezione INFN di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
c Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy
d Institute of Mathematics, Ufa Scientific Center, Russian Academy of Sciences, 112 Chernyshevsky Str., Ufa 450008, Russia

Abstract: In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal $H^{4}$ equations and the $H^{6}$ equations. These solutions are obtained exploiting the properties of the first integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov R.I., J. Phys. A: Math. Theor. 50 (2017), 345205, 26 pages]. These first integrals are used to reduce the problem to the solution of some linear or linearizable non-autonomous ordinary difference equations which can be formally solved.

Keywords: quad-equations; Darboux integrability; exact solutions; CAC.

Funding Agency Grant Number
Instituto Nazionale di Fisica Nucleare IS-CSN4
Australian Research Council FL120100094
GG has been supported by INFN IS-CSN4 Mathematical Methods of Nonlinear Physics and by the Australian Research Council through an Australian Laureate Fellowship grant FL120100094.


DOI: https://doi.org/10.3842/SIGMA.2018.008

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MSC: 37K10; 37L60; 39A14
Received: April 26, 2017; in final form January 16, 2018; Published online February 2, 2018
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Citation: 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.

Citation in format AMSBIB
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\by Giorgio~Gubbiotti, Christian~Scimiterna, Ravil~I.~Yamilov
\paper Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions
\jour SIGMA
\yr 2018
\vol 14
\papernumber 008
\totalpages 51
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\crossref{https://doi.org/10.3842/SIGMA.2018.008}
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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. Kassotakis P., Nieszporski M., “Difference Systems in Bond and Face Variables and Non-Potential Versions of Discrete Integrable Systems”, J. Phys. A-Math. Theor., 51:38 (2018), 385203  crossref  isi
    2. Habibullin I.T., Poptsova M.N., “Algebraic Properties of Quasilinear Two-Dimensional Lattices Connected With Integrability”, Ufa Math. J., 10:3 (2018), 86–105  mathnet  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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