Аннотация:
A symmetry classification is performed for a class of differential-difference equations depending on 9 parameters. A 6-parameter subclass of these equations is an integrable discretization of the Krichever–Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1⩽n⩽5. The highest dimensions, namely n=5 and n=4 occur only in the integrable cases.
Образец цитирования:
Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 097, 16 pp.
\RBibitem{LevWinYam11}
\by Decio Levi, Pavel Winternitz, Ravil I. Yamilov
\paper Symmetries of the Continuous and Discrete Krichever--Novikov Equation
\jour SIGMA
\yr 2011
\vol 7
\papernumber 097
\totalpages 16
\mathnet{http://mi.mathnet.ru/sigma655}
\crossref{https://doi.org/10.3842/SIGMA.2011.097}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2861179}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000296080200001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857090428}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma655
https://www.mathnet.ru/rus/sigma/v7/p97
Эта публикация цитируется в следующих 11 статьяx:
V. E. Adler, “Negative flows and non-autonomous reductions of the Volterra lattice”, Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of... (2024)
Б. И. Сулейманов, А. М. Шавлуков, “Интегрируемое уравнение Абеля и асимптотики симметрийных решений уравнения Кортевега-де Вриза”, Уфимск. матем. журн., 13:2 (2021), 104–111; B. I. Suleimanov, A. M. Shavlukov, “Integrable Abel equation and asymptotics
of symmetry solutions of Korteweg-de Vries equation”, Ufa Math. J., 13:2 (2021), 99–106
Dorodnitsyn V.A. Kaptsov I E., “Shallow Water Equations in Lagrangian Coordinates: Symmetries, Conservation Laws and Its Preservation in Difference Models”, Commun. Nonlinear Sci. Numer. Simul., 89 (2020), 105343
Habibullin I.T., Khakimova A.R., “On the Recursion Operators For Integrable Equations”, J. Phys. A-Math. Theor., 51:42 (2018), 425202
Gubbiotti G., Scimiterna C., Levi D., “The Non-Autonomous Ydkn Equation and Generalized Symmetries of Boll Equations”, J. Math. Phys., 58:5 (2017), 053507
Kou K., Li J., “Exact Traveling Wave Solutions of the Krichever-Novikov Equation: a Dynamical System Approach”, Int. J. Bifurcation Chaos, 27:4 (2017), 1750058
Anco S.C., Avdonina E.D., Gainetdinova A., Galiakberova L.R., Ibragimov N.H., Wolf T., “Symmetries and Conservation Laws of the Generalized Krichever-Novikov Equation”, J. Phys. A-Math. Theor., 49:10, SI (2016), 105201
Gungor F., Ozemir C., “Lie Symmetries of a Generalized Kuznetsov-Zabolotskaya-Khokhlov Equation”, J. Math. Anal. Appl., 423:1 (2015), 623–638
Levi D., Ricca E., Thomova Z., Winternitz P., “Lie Group Analysis of a Generalized Krichever-Novikov Differential-Difference Equation”, J. Math. Phys., 55:10 (2014), 103503
Demskoi D.K., Viallet C.-M., “Algebraic Entropy for Semi-Discrete Equations”, J. Phys. A-Math. Theor., 45:35 (2012), 352001
Levi D., Scimiterna Ch., “Classification of Multilinear Real Quadratic Partial Difference Equations Linearizable by Point and Hopf-Cole Transformations”, Int. J. Geom. Methods Mod. Phys., 9:2, SI (2012), 1260004
Цитирование в формате AMSBIB
Обратная связь: