Аннотация:
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.
GG has been supported by INFN IS-CSN4 Mathematical Methods of Nonlinear Physics
and by the Australian Research Council through an Australian Laureate Fellowship grant
FL120100094.
Поступила:26 апреля 2017 г.; в окончательном варианте 16 января 2018 г.; опубликована 2 февраля 2018 г.
Образец цитирования:
Giorgio Gubbiotti, Christian Scimiterna, Ravil I. Yamilov, “Darboux Integrability of Trapezoidal H4 and H6 Families of Lattice Equations II: General Solutions”, SIGMA, 14 (2018), 008, 51 pp.
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\paper Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions
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Эта публикация цитируется в следующих 10 статьяx:
Giorgio Gubbiotti, Andrew P Kels, Claude-M Viallet, “Algebraic entropy for hex systems”, Nonlinearity, 37:12 (2024), 125007
D.-d. Zhang, D.-j. Zhang, P. H. van der Kamp, “From auto-Backlund transformations to auto-Backlund transformations, and torqued abs equations”, Math. Phys. Anal. Geom., 24:4 (2021), 33
G. Gubbiotti, A. P. Kels, “Algebraic entropy for face-centered quad equations”, J. Phys. A-Math. Theor., 54:45 (2021), 455201
И. Т. Хабибуллин, М. Н. Кузнецова, “О классификационном алгоритме интегрируемых двумеризованных цепочек на основе алгебр Ли–Райнхарта”, ТМФ, 203:1 (2020), 161–173; I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices
via Lie–Rinehart algebras”, Theoret. and Math. Phys., 203:1 (2020), 569–581
Dan-Da Zhang, Peter H. van der Kamp, Da-Jun Zhang, “Multi-Component Extension of CAC Systems”, SIGMA, 16 (2020), 060, 30 pp.
I. T. Habibullin, M. N. Kuznetsova, A. U. Sakieva, “Integrability conditions for two-dimensional Toda-like equations”, J. Phys. A-Math. Theor., 53:39 (2020), 395203
R. N. Garifullin, R. I. Yamilov, “On series of Darboux integrable discrete equations on square lattice”, Уфимск. матем. журн., 11:3 (2019), 100–109; Ufa Math. J., 11:3 (2019), 99–108
Kassotakis P., Nieszporski M., “Difference Systems in Bond and Face Variables and Non-Potential Versions of Discrete Integrable Systems”, J. Phys. A-Math. Theor., 51:38 (2018), 385203
Habibullin I.T., Poptsova M.N., “Algebraic Properties of Quasilinear Two-Dimensional Lattices Connected With Integrability”, Ufa Math. J., 10:3 (2018), 86–105
Giorgio Gubbiotti, Symmetries and Integrability of Difference Equations, 2017, 75
Цитирование в формате AMSBIB
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