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Ufimsk. Mat. Zh., 2009, Volume 1, Issue 2, Pages 101–105 (Mi ufa13)  

This article is cited in 8 scientific papers (total in 8 papers)

On a nonlinear integrable difference equation on the square

D. Leviab, R. I. Yamilovc

a Sezione INFN
b Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre
c Ufa Institute of Mathematics, Russian Academy of Sciences

Abstract: We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra differential-difference equations. This equation is not symmetric with respect to the exchange of the two discrete variables. Its integrability is proved by constructing its Lax pair.

Keywords: nonlinear integrable difference equation, Lax pair, Miura transformation, Volterra equation.

Full text: PDF file (373 kB)
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Bibliographic databases:

UDC: 517.9
Received: 27.04.2009
Language:

Citation: D. Levi, R. I. Yamilov, “On a nonlinear integrable difference equation on the square”, Ufimsk. Mat. Zh., 1:2 (2009), 101–105

Citation in format AMSBIB
\Bibitem{LevYam09}
\by D.~Levi, R.~I.~Yamilov
\paper On a nonlinear integrable difference equation on the square
\jour Ufimsk. Mat. Zh.
\yr 2009
\vol 1
\issue 2
\pages 101--105
\mathnet{http://mi.mathnet.ru/ufa13}
\zmath{https://zbmath.org/?q=an:1240.39020}
\elib{http://elibrary.ru/item.asp?id=12501233}


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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. Boll R., “Classification of 3D Consistent Quad-Equations”, J. Nonlinear Math. Phys., 18:3 (2011), 337–365  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Levi D., Yamilov R.I., “Generalized Symmetry Integrability Test for Discrete Equations on the Square Lattice”, J. Phys. A-Math. Theor., 44:14 (2011), 145207  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Boll R., Suris Yu.B., “On the Lagrangian Structure of 3D Consistent Systems of Asymmetric Quad-Equations”, J. Phys. A-Math. Theor., 45:11 (2012), 115201  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Boll R., “On Bianchi Permutability of Backlund Transformations for Asymmetric Quad-Equations”, J. Nonlinear Math. Phys., 20:4 (2013), 577–605  crossref  mathscinet  isi  elib
    5. Samajdar R., Jain S.R., “a Nodal Domain Theorem For Integrable Billiards in Two Dimensions”, Ann. Phys., 351 (2014), 1–12  crossref  mathscinet  isi
    6. Scimiterna Ch., Hay M., Levi D., “on the Integrability of a New Lattice Equation Found By Multiple Scale Analysis”, J. Phys. A-Math. Theor., 47:26 (2014), 265204  crossref  mathscinet  zmath  isi  elib
    7. Garifullin R.N., Yamilov R.I., “Integrable Discrete Nonautonomous Quad-Equations as Backlund Auto-Transformations For Known Volterra and Toda Type Semidiscrete Equations”, Seventh International Workshop: Group Analysis of Differential Equations and Integrable Systems (Gadeisvii), Journal of Physics Conference Series, 621, IOP Publishing Ltd, 2015, UNSP 012005  crossref  isi
    8. Garifullin R.N., Yamilov R.I., Levi D., “Classification of Five-Point Differential-Difference Equations”, J. Phys. A-Math. Theor., 50:12 (2017), 125201  crossref  mathscinet  zmath  isi  scopus
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