|
This article is cited in 24 scientific papers (total in 24 papers)
Recursion operators, conservation laws, and integrability conditions for difference equations
A. V. Mikhailova, J. P. Wangb, P. Xenitidisa
a Applied Mathematics Department, University of Leeds, UK
b School of Mathematics and Statistics, University of Kent, UK
Abstract:
We attempt to propose an algebraic approach to the theory of integrable difference equations. We define the concept of a recursion operator for difference equations and show that it generates an infinite sequence of symmetries and canonical conservation laws for a difference equation. As in the case of partial differential equations, these canonical densities can serve as integrability conditions for difference equations. We obtain the recursion operators for the Viallet equation and all the Adler–Bobenko–Suris equations.
Keywords:
difference equation, integrability, integrability condition, symmetry,
conservation law, recursion operator
DOI:
https://doi.org/10.4213/tmf6624
 Full text:
PDF file (600 kB)
References:
PDF file
HTML file
English version:
Theoretical and Mathematical Physics, 2011, 167:1, 421–443
Bibliographic databases:
   
Received: 15.11.2010
Citation:
A. V. Mikhailov, J. P. Wang, P. Xenitidis, “Recursion operators, conservation laws, and integrability conditions for difference equations”, TMF, 167:1 (2011), 23–49; Theoret. and Math. Phys., 167:1 (2011), 421–443
Citation in format AMSBIB
\Bibitem{MikWanXen11}
\by A.~V.~Mikhailov, J.~P.~Wang, P.~Xenitidis
\paper Recursion operators, conservation laws, and integrability conditions for difference equations
\jour TMF
\yr 2011
\vol 167
\issue 1
\pages 23--49
\mathnet{http://mi.mathnet.ru/tmf6624}
\crossref{https://doi.org/10.4213/tmf6624}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3165750}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011TMP...167..421M}
\transl
\jour Theoret. and Math. Phys.
\yr 2011
\vol 167
\issue 1
\pages 421--443
\crossref{https://doi.org/10.1007/s11232-011-0033-y}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000291480500002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79956077604}
Linking options:
http://mi.mathnet.ru/eng/tmf6624https://doi.org/10.4213/tmf6624 http://mi.mathnet.ru/eng/tmf/v167/i1/p23
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:
-
Decio Levi, Christian Scimiterna, “Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf–Cole Transformations”, SIGMA, 7 (2011), 079, 24 pp.
 -
Mikhailov A.V., Wang J.P., “A new recursion operator for Adler's equation in the Viallet form”, Phys. Lett. A, 375:45 (2011), 3960–3963
  -
Xenitidis P., “Symmetries and conservation laws of the ABS equations and corresponding differential-difference equations of Volterra type”, J. Phys. A, 44:43 (2011), 435201, 22 pp.
-
Mikhailov A.V., Wang J.P., Xenitidis P., “Cosymmetries and Nijenhuis recursion operators for difference equations”, Nonlinearity, 24:7 (2011), 2079–2097
-
Wang J.P., “Recursion operator of the Narita-Itoh-Bogoyavlensky lattice”, Stud. Appl. Math., 129:3 (2012), 309–327
-
Demskoi D.K. Viallet C.-M., “Algebraic entropy for semi-discrete equations”, J. Phys. A, 45:35 (2012), 352001, 10 pp.
-
Garifullin R.N. Yamilov R.I., “Generalized symmetry classification of discrete equations of a class depending on twelve parameters”, J. Phys. A, 45:34 (2012), 345205, 23 pp.
-
Xenitidis P., Nijhoff F., “Symmetries and conservation laws of lattice Boussinesq equations”, Phys. Lett. A, 376:35 (2012), 2394–2401
-
F. Khanizadeh, A. V. Mikhailov, Jing Ping Wang, “Darboux transformations and recursion operators for differential–difference equations”, Theoret. and Math. Phys., 177:3 (2013), 1606–1654
-
I. T. Habibullin, M. V. Yangubaeva, “Formal diagonalization of a discrete Lax operator and conservation laws and symmetries of dynamical systems”, Theoret. and Math. Phys., 177:3 (2013), 1655–1679
-
Cheng J., Zhang D., “Conservation Laws of Some Lattice Equations”, Front. Math. China, 8:5, SI (2013), 1001–1016
-
Grant T.J., Hydon P.E., “Characteristics of Conservation Laws for Difference Equations”, Found. Comput. Math., 13:4 (2013), 667–692
-
Zhang D.-j., Cheng J.-w., Sun Y.-y., “Deriving Conservation Laws for Abs Lattice Equations From Lax pairs”, J. Phys. A-Math. Theor., 46:26 (2013), 265202
-
Sergey Ya. Startsev, “Non-Point Invertible Transformations and Integrability of Partial Difference Equations”, SIGMA, 10 (2014), 066, 13 pp.
-
R. N. Garifullin, A. V. Mikhailov, R. I. Yamilov, “Discrete equation on a square lattice with a nonstandard structure of generalized symmetries”, Theoret. and Math. Phys., 180:1 (2014), 765–780
-
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
-
Mikhailov A.V., Xenitidis P., “Second Order Integrability Conditions For Difference Equations: An Integrable Equation”, Lett. Math. Phys., 104:4 (2014), 431–450
-
Startsev S.Ya., “Darboux Integrable Discrete Equations Possessing An Autonomous First-Order Integral”, J. Phys. A-Math. Theor., 47:10 (2014), 105204
-
Demskoi D.K., “Quad-Equations and Auto-Backlund Transformations of NLS-Type Systems”, J. Phys. A-Math. Theor., 47:16 (2014), 165204
-
Habibullin I.T. Poptsova M.N., “Asymptotic Diagonalization of the Discrete Lax pair Around Singularities and Conservation Laws For Dynamical Systems”, J. Phys. A-Math. Theor., 48:11 (2015), 115203
-
Mikhailov A.V. Papamikos G. Wang J.P., “Darboux Transformation for the Vector sine-Gordon Equation and Integrable Equations on a Sphere”, Lett. Math. Phys., 106:7 (2016), 973–996
-
Hietarinta J. Joshi N. Nijhoff F., “Discrete Systems and Integrability”, Discrete Systems and Integrability, Cambridge Texts in Applied Mathematics, Cambridge Univ Press, 2016, 1–445
-
Lou S. Shi Y. Zhang D.-j., “Spectrum transformation and conservation laws of lattice potential KdV equation”, Front. Math. China, 12:2 (2017), 403–416
-
Xenitidis P., “Determining the Symmetries of Difference Equations”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 474:2219 (2018), 20180340
|
| Number of views: |
| This page: | 511 | | Full text: | 92 | | References: | 46 | | First page: | 21 |
|
Terms of Use