In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal H4 equations and the H6 equations. These solutions are obtained exploiting the properties of the first integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov R.I., J. Phys. A: Math. Theor. 50 (2017), 345205, 26 pages]. These first integrals are used to reduce the problem to the solution of some linear or linearizable non-autonomous ordinary difference equations which can be formally solved.

Gubbiotti, G., Scimiterna, C., Yamilov, R.I. (2018). Darboux integrability of trapezoidal H4 and H6 families of lattice equations II: General solutions. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 14 [10.3842/SIGMA.2018.008].

Darboux integrability of trapezoidal H4 and H6 families of lattice equations II: General solutions

Gubbiotti G.;Scimiterna C.;Yamilov R. I.
2018-01-01

Abstract

In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal H4 equations and the H6 equations. These solutions are obtained exploiting the properties of the first integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov R.I., J. Phys. A: Math. Theor. 50 (2017), 345205, 26 pages]. These first integrals are used to reduce the problem to the solution of some linear or linearizable non-autonomous ordinary difference equations which can be formally solved.
2018
Gubbiotti, G., Scimiterna, C., Yamilov, R.I. (2018). Darboux integrability of trapezoidal H4 and H6 families of lattice equations II: General solutions. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 14 [10.3842/SIGMA.2018.008].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/365890
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