Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case

• Autorzy: Ndogmo J.-C.

Identyfikatory

DOI

10.1515/jaa-2018-0017

• Języki publikacji: EN

Abstrakty

EN

Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. Adiscussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations.

Słowa kluczowe

EN

maximal symmetry algebra; variational symmetry; divergence symmetry; first integrals

PL

symetria wariacyjna; symetria rozbieżności; całka pierwsza

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2018
• Tom: Vol. 24, nr 2
• Strony: 175--183
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Ndogmo J.-C.

• Department of Mathematics and Applied Mathematics, University of Venda, P/B X5050, Thohoyandou, Limpopo 0950, South Africa

Bibliografia

• [1] J. Krause and L. Michel, Equations différentielles linéaires d’ordre n > 2 ayant une algèbre de Lie de symétrie de dimension n + 4, C. R. Math. Acad. Sci. Paris 307 (1988), 905-910.
• [2] S. Lie, Klassification und Integration von gewöhnlichen Differentialgleichungen zwischen x, y, die eine Gruppe von Transformationen gestatten. I, Math. Ann. 22 (1888), 213-253.
• [3] F. M. Mahomed and P. G. L. Leach, Symmetry lie algebras of nth order ordinary differential equations, J. Math. Anal. Appl. 151 (1990), 80-107.
• [4] J. C. Ndogmo, Generation and identification of ordinary differential equations of maximal symmetry algebra, Abstr. Appl. Anal. 2016 (2016), Article ID 1796316.
• [5] J. C. Ndogmo, Some variational principles associated with ODEs of maximal symmetry. Part 1: Equations in canonical form, J. Appl. Anal. 24 (2018), DOI 10.1515/jaa-2018-0002.
• [6] J. C. Ndogmo and F. M. Mahomed, On certain properties of linear iterative equations, Cent. Eur. J. Math. 12 (2014), 648-657.
• [7] P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986.
• [8] P. J. Olver, Differential invariants and invariant differential equations, Lie Groups Appl. 1 (1994), 177-192.
• [9] P. J. Olver, Equivalence, Invariants, and Symmetry, Cambridge University Press, Cambridge, 1995.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).