Аннотация:
Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are used to construct new examples of integrable equations and autotransformations of the Hietarinta equation.
Образец цитирования:
Sergey Ya. Startsev, “On Non-Point Invertible Transformations of Difference and Differential-Difference Equations”, SIGMA, 6 (2010), 092, 14 pp.
\RBibitem{Sta10}
\by Sergey Ya.~Startsev
\paper On Non-Point Invertible Transformations of Difference and Differential-Difference Equations
\jour SIGMA
\yr 2010
\vol 6
\papernumber 092
\totalpages 14
\mathnet{http://mi.mathnet.ru/sigma550}
\crossref{https://doi.org/10.3842/SIGMA.2010.092}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2769923}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000285631500004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958787578}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma550
https://www.mathnet.ru/rus/sigma/v6/p92
Эта публикация цитируется в следующих 16 статьяx:
Р. Н. Гарифуллин, “Классификация полудискретных уравнений гиперболического типа. Случай симметрий пятого порядка”, ТМФ, 222:1 (2025), 14–24; R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of fifth-order symmetries”, Theoret. and Math. Phys., 222:1 (2025), 10–19
S. Ya. Startsev, “On Darboux non-integrability of Hietarinta equation”, Уфимск. матем. журн., 13:2 (2021), 166–175; Ufa Math. J., 13:2 (2021), 160–169
Р. Н. Гарифуллин, Р. И. Ямилов, “Модифицированные серии интегрируемых дискретных уравнений на квадратной решетке с нестандартной симметрийной структурой”, ТМФ, 205:1 (2020), 23–40; R. N. Garifullin, R. I. Yamilov, “Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure”, Theoret. and Math. Phys., 205:1 (2020), 1264–1278
Grammaticos B., Ramani A., “Gambier Lattices and Other Linearisable Systems”, J. Nonlinear Math. Phys., 27:4 (2020), 688–696
Garifullin R.N. Gubbiotti G. Yamilov I R., “Integrable Discrete Autonomous Quad-Equations Admitting, as Generalized Symmetries, Known Five-Point Differential-Difference Equations”, J. Nonlinear Math. Phys., 26:3 (2019), 333–357
Rustem N. Garifullin, Ravil I. Yamilov, “Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation”, SIGMA, 15 (2019), 062, 15 pp.
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
Gubbiotti, G.; Levi, D.l Scimiterna, C., “On partial differential and difference equations with symmetries depending on arbitrary functions”, Acta Polytechnica, 56:3 (2016), 193-201
Garifullin R.N. Yamilov R.I., “Integrable Discrete Nonautonomous Quad-Equations as Backlund Auto-Transformations For Known Volterra and Toda Type Semidiscrete Equations”, Seventh International Workshop: Group Analysis of Differential Equations and Integrable Systems (Gadeisvii), Journal of Physics Conference Series, 621, IOP Publishing Ltd, 2015, UNSP 012005
Sergey Ya. Startsev, “Non-Point Invertible Transformations and Integrability of Partial Difference Equations”, SIGMA, 10 (2014), 066, 13 pp.
Startsev S.Ya., “Darboux Integrable Discrete Equations Possessing an Autonomous First-Order Integral”, J. Phys. A-Math. Theor., 47:10 (2014), 105204
С. Я. Старцев, “Интегрируемые по Дарбу дифференциально-разностные уравнения, допускающие интеграл первого порядка”, Уфимск. матем. журн., 4:3 (2012), 161–176
Garifullin R.N. Yamilov R.I., “Generalized Symmetry Classification of Discrete Equations of a Class Depending on Twelve Parameters”, J. Phys. A-Math. Theor., 45:34 (2012), 345205
Maheswari C.U., Sahadevan R., “On the conservation laws for nonlinear partial difference equations”, Journal of Physics A-Mathematical and Theoretical, 44:27 (2011), 275203
Decio Levi, Christian Scimiterna, “Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf–Cole Transformations”, SIGMA, 7 (2011), 079, 24 pp.
Habibullin I., Zheltukhina N., Sakieva A., “Discretization of hyperbolic type Darboux integrable equations preserving integrability”, J Math Phys, 52:9 (2011), 093507
Цитирование в формате AMSBIB
Обратная связь: