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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 3, Pages 177–183 (Mi ufa161)  

This article is cited in 3 scientific papers (total in 3 papers)

Examples of Darboux integrable discrete equations possessing first integrals of an arbitrarily high minimal order

R. N. Garifullin, R. I. Yamilov

Ufa Institute of Mathematics, Russian Academy of Sciences, Ufa, Russian Federation

Abstract: We consider a discrete equation, defined on the two-dimensional square lattice, which is linearizable, namely, of the Burgers type and depends on a parameter $\alpha$. For any natural number $N$ we choose $\alpha$ so that the equation becomes Darboux integrable and the minimal orders of its first integrals in both directions are greater or equal than $N$.

Keywords: discrete equation, Darboux integrability, first integral.

Full text: PDF file (442 kB)
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UDC: 517.929
Received: 12.07.2012
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Citation: R. N. Garifullin, R. I. Yamilov, “Examples of Darboux integrable discrete equations possessing first integrals of an arbitrarily high minimal order”, Ufimsk. Mat. Zh., 4:3 (2012), 177–183

Citation in format AMSBIB
\Bibitem{GarYam12}
\by R.~N.~Garifullin, R.~I.~Yamilov
\paper Examples of Darboux integrable discrete equations possessing first integrals of an arbitrarily high minimal order
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 3
\pages 177--183
\mathnet{http://mi.mathnet.ru/ufa161}


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    This publication is cited in the following articles:
    1. M. V. Yangubaeva, “On structure of integrals for systems of discrete equations”, Ufa Math. J., 6:1 (2014), 111–116  mathnet  crossref  elib
    2. 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  scopus
    3. S. Ya. Startsev, “Relationships Between Symmetries Depending on Arbitrary Functions and Integrals of Discrete Equations”, J. Phys. A-Math. Theor., 50:50 (2017), 50LT01  crossref  mathscinet  zmath  isi  scopus
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