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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 152, Pages 159–164 (Mi into359)  

On the Integrability of a Lattice Equation with Two Continuum Limits

R. N. Garifullin, R. I. Yamilov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa

Abstract: We study a new example of lattice equation being one of the key equations of a recent generalized symmetry classification of five-point differential-difference equations. This equation has two different continuum limits, which are the well-known fifth-order partial-differential equations, namely, the Sawada–Kotera and KaupЦ-Kupershmidt equations. We justify its integrability by constructing an $L$-$A$ pair and a hierarchy of conservation laws.

Keywords: differential-difference equation, integrability, Lax pair, conservation law

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Bibliographic databases:
UDC: 517.547
MSC: 37K10, 35G50, 39A10

Citation: R. N. Garifullin, R. I. Yamilov, “On the Integrability of a Lattice Equation with Two Continuum Limits”, Mathematical physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 152, VINITI, Moscow, 2018, 159–164

Citation in format AMSBIB
\Bibitem{GarYam18}
\by R.~N.~Garifullin, R.~I.~Yamilov
\paper On the Integrability of a Lattice Equation with Two Continuum Limits
\inbook Mathematical physics
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 152
\pages 159--164
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into359}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3903386}


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