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.
Darboux integrability of trapezoidal H4 and H6 families of lattice equations II: General solutions / G. Gubbiotti, C. Scimiterna, R.I. Yamilov. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 14(2018), pp. 008.1-008.51. [10.3842/SIGMA.2018.008]
Darboux integrability of trapezoidal H4 and H6 families of lattice equations II: General solutions
G. Gubbiotti;
2018
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.File | Dimensione | Formato | |
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