Geodesic
Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we construct the general solutions of two families of quad-equations, namely the trapezoidal $H^{4}$ equations and the $H^{6}$ 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.
Keywords: quad-equations; Darboux integrability; exact solutions; CAC. 
@article{SIGMA_2018_14_a7,
     author = {Giorgio Gubbiotti and Christian Scimiterna and Ravil I. Yamilov},
     title = {Darboux {Integrability} of {Trapezoidal} $H^{4}$ and $H^{6}$ {Families} of {Lattice} {Equations} {II:} {General} {Solutions}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2018},
     volume = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a7/}
}
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Giorgio Gubbiotti; Christian Scimiterna; Ravil I. Yamilov. Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a7/

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