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2014 | 12 | 4 | 648-657
Tytuł artykułu

On certain properties of linear iterative equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained, and this gives rise to the derivation of important symmetry properties for iterative equations. The transformation mapping a given iterative equation to the canonical form is obtained in terms of the simplest determining equation, and several examples of application are discussed.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
4
Strony
648-657
Opis fizyczny
Daty
wydano
2014-04-01
online
2014-01-17
Twórcy
Bibliografia
  • [1] Cariñena J.F., Grabowski J., de Lucas J., Superposition rules for higher-order systems and their applications, J. Phys. A, 2012, 45(18), #185202 http://dx.doi.org/10.1088/1751-8113/45/18/185202
  • [2] Krause J., Michel L., Equations différentielles linéaires d’ordre n > 2 ayant une algèbre de Lie de symétrie de dimension n + 4, C. R. Acad. Sci. Paris, 1988, 307(18), 905–910
  • [3] Krause J., Michel L., Classification of the symmetries of ordinary differential equations, In: Group Theoretical Methods in Physics, Moscow, June 4–9, 1990, Lecture Notes in Phys., 382, Springer, Berlin, 1991, 251–262
  • [4] Leach P.G.L., Andriopoulos K., The Ermakov equation: a commentary, Appl. Anal. Discrete Math., 2008, 2(2), 146–157 http://dx.doi.org/10.2298/AADM0802146L
  • [5] Lie S., Classification und Integration von gewöhnlichen Differentialgleichungen zwischen xy, die eine Gruppe von Transformationen gestatten. III, Archiv for Mathematik og Naturvidenskab, 1883, 8, 371–458
  • [6] Lie S., Classification und Integration von gewöhnlichen Differentialgleichungen zwischen xy, die eine Gruppe von Transformationen gestetten, Math. Ann., 1888, 32(2), 213–281 http://dx.doi.org/10.1007/BF01444068
  • [7] de Lucas J., Sardón C., On Lie systems and Kummer-Schwarz equations, J. Math. Phys., 2013, 54(3), #033505 http://dx.doi.org/10.1063/1.4794280
  • [8] Mahomed F.M., Leach P.G.L., Symmetry Lie algebras of nth order ordinary differential equations, J. Math. Anal. Appl., 1990, 151(1), 80–107 http://dx.doi.org/10.1016/0022-247X(90)90244-A
  • [9] Ndogmo J.C., Equivalence transformations of the Euler-Bernoulli equation, Nonlinear Anal. Real World Appl., 2012, 13(5), 2172–2177 http://dx.doi.org/10.1016/j.nonrwa.2012.01.012
  • [10] Ndogmo J.C., Some results on equivalence groups, J. Appl. Math., 2012, #484805
  • [11] Schwarz F., Solving second order ordinary differential equations with maximal symmetry group, Computing, 1999, 62(1), 1–10 http://dx.doi.org/10.1007/s006070050009
  • [12] Schwarz F., Equivalence classes, symmetries and solutions of linear third-order differential equations, Computing, 2002, 69(2), 141–162 http://dx.doi.org/10.1007/s00607-002-1454-0
  • [13] Sebbar A., Sebbar A., Eisenstein series and modular differential equations, Canad. Math. Bull., 2012, 55(2), 400–409 http://dx.doi.org/10.4153/CMB-2011-091-3
  • [14] Tsitskishvili A., Solution of the Schwarz differential equation, Mem. Differential Equations Math. Phys., 1997, 11, 129–156
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0364-z
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