In this paper we construct a non-autonomous version of the Hietarinta equation [Hietarinta J., J. Phys. A: Math. Gen. 37 (2004), L67-L73] and study its integrability properties. We show that this equation possess linear growth of the degrees of iterates, generalized symmetries depending on arbitrary functions, and that it is Darboux integrable. We use the first integrals to provide a general solution of this equation. In particular we show that this equation is a sub-case of the non-autonomous QV equation, and we provide a nonautonomous Möbius transformation to another equation found in [Hietarinta J., J. Nonlinear Math. Phys. 12 (2005), suppl. 2, 223-230] and appearing also in Boll’s classification [Boll R., Ph.D. Thesis, Technische Universität Berlin, 2012].

Gubbiotti, G., Scimiterna, C. (2018). Reconstructing a lattice equation: A non-autonomous approach to the Hietarinta equation. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 14 [10.3842/SIGMA.2018.004].

Reconstructing a lattice equation: A non-autonomous approach to the Hietarinta equation

Gubbiotti G.;Scimiterna C.
2018-01-01

Abstract

In this paper we construct a non-autonomous version of the Hietarinta equation [Hietarinta J., J. Phys. A: Math. Gen. 37 (2004), L67-L73] and study its integrability properties. We show that this equation possess linear growth of the degrees of iterates, generalized symmetries depending on arbitrary functions, and that it is Darboux integrable. We use the first integrals to provide a general solution of this equation. In particular we show that this equation is a sub-case of the non-autonomous QV equation, and we provide a nonautonomous Möbius transformation to another equation found in [Hietarinta J., J. Nonlinear Math. Phys. 12 (2005), suppl. 2, 223-230] and appearing also in Boll’s classification [Boll R., Ph.D. Thesis, Technische Universität Berlin, 2012].
2018
Gubbiotti, G., Scimiterna, C. (2018). Reconstructing a lattice equation: A non-autonomous approach to the Hietarinta equation. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 14 [10.3842/SIGMA.2018.004].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/365889
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