On Construction of the First-Order Differential Equations in the Space M(1,3) x R(u) with Non-trivial Symmetry

• Autorzy: Fedorchuk V. , Fedorchuk V.
• Konferencja: X Polish-Czech Mathematical School (10 ; 04-07.06.2003 ; Poraj near Częstochowa, Poland)
• Języki publikacji: EN

Abstrakty

EN

We have constructed the first-order differential equations invariant under non-splitting subgroups of the group P(1,4) and defined in the space M(1,3) x R(u). The results obtained can be used in relativistic and non-relativistic physics.

Słowa kluczowe

EN

first-order differential equation; Lie algebra

PL

równanie różniczkowe pierwszego rzędu; algebra Liego

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2003
• Tom: Vol. 9
• Strony: 35--39
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Fedorchuk V.

• Pedagogical Academy, Institute of Mathematics, Podchorążych 2, 30-084, Kraków, Poland
• Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of the National Ukrainian Academy of Sciences, Naukova Street 3b, 79601 Lviv, Ukraine

autor

Fedorchuk V.

• Franko Lviv National University, Universytecka Street 1, 79000 Lviv, Ukraine

Bibliografia

• [1] L.V. Ovsiannikov, Group Analysis oj Differential Equations, Academic Press, New York, 1982.
• [2] V.I. Fushchych, W.M. Shtelen and N.I. Serov, Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, Dordrecht, Kluver Academic Publishers, 1993.
• [3] V.I. Fushchych and A.G. Nikitin, Symmetries oj Equations of Quantum, Mechanics, Allerton Press Inc., New York, 1994.
• [4] V.I. Fushchich, A.F. Barannik. L.F. Barannik and V.M. Fedorchuk, Continuous subgroups of the Poincaré group P (1, 4), J. Phys. Math. Gen., Vol. 18, No. 14, 2893-2899, 1985.
• [5] V.I. Fedorchuk, On Differential Equations of First- and Second-Order in the Space M (1, 3) x R( u) with Nontrivial Symmetry Groups, Proc. of the Fourth Internat. Conf. Symmetry in Nonlinear Mathematical Physics (9-15 July 2001, Kyiv, Ukraine), Proceedings of Institute of Mathematics NAS of Ukraine, Kyiv, 43, Part 1, 145-148, 2001.
• [6] S. Lie, Ȕber Differentialinvarianten, Math. Ann. V. 24, N 1, 52-89, 1884.