Nonlinear representations of the conformal algebra AC(1,2) for quasilinear second-order differential equations

Blazhko Lyudmila Mykolayivna

Blazhko Lyudmila Mykolayivna ¹

¹ Department of Higher Mathematics, Kyiv National University of Civil Engineering and Architecture, Kyiv, 03037, Ukraine

Keywords: nonlinear representations, quasilinear second-order differential equations, the Poincare algebra

Download

Abstract

The article presents all possible representations of the Poincare algebra, extended Poincare algebra and conformal algebra, under which quasi-linear differential equations with the second- order partial derivatives are invariant in the case of three independent variables.

References

[1] Barbashov B. M., Nesterenko V. V. V. Relativistic string model in hadron physics. Moscow: Energoatomizdat, 1987. 176 p.

[2] Barbashov B. M., Chernikov N. A. Solution and quantization of a nonlinear two-dimensional model of Born-Infeld type // Journal of Experimental and Theoretical Physics. 1966. Т. 60, № 5. P. 1296-1308.

[3] Blazhko L. M. Invariance of a quasilinear equation of the second order with respect to conformal algebra // Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. - 2001. - Т. 36. - P. 40-44.

[4] Blazhko L. M. Symmetric properties and exact solutions of nonlinear equations of hyperbolic type: PhD in Physics and Mathematics: 01.01.03 / - К., 2008. - 138 p.

[5] Lagno V.I., Spichak S.V., Stogniy V.I. Symmetric analysis of evolutionary type equations // Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine: Mathematics and its applications. - 2002. - Vol. 45. - 359 p.

[6] Ovsiannikov L.V. Group analysis of differential equations. - New York : Academic Press, 1982. - 400 p.

[7] Serov M. I., Blazhko L. M. Conformal invariance of quasilinear differential equations with partial differentials of the second order // Scientific Bulletin of Uzhhorod University. Ser. math. and Informatics - Uzhhorod: UzhNU Publishing House “Goverla”, 2012. - Vol. 23, № 1. - P. 26.

[8] Fushchich V. I. I., Shteleni V. M., Serov N. I. Symmetry analysis and exact solutions of equations of nonlinear mathematical physics. К. Nauk. dumka, 1989. 339 p.

[9] Wisem D. Linear and Nonlinear Waves. М. : Mir, 1977. 622 p.

[10] Akhatov I.S., Gazizov R.K., Ibragimov N.H., Nonlocal symmetries. Heuristic approach // J. Sov. Math. – 55 (1991) – P. 1401-1450.

[11] Rideau G. and Winternitz P. Nonlinear equations invariant under Poincare, similitude and conformal groups in two-dimensional space-time // J. Math. Phys., 1990. - V.31 - P. 1095–1105.

[12] Fushchych W.I. Symmetry of equations of linear and nonlinear quantum mechanics // Scientific Works, 2004. - V. 6 - P. 105-119.

Download

Cite

ACS Style: Blazhko, L.M. Nonlinear representations of the conformal algebra AC(1,2) for quasilinear second-order differential equations. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Blazhko LM. Nonlinear representations of the conformal algebra AC(1,2) for quasilinear second-order differential equations. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style: Lyudmila Mykolayivna Blazhko. 2016. "Nonlinear representations of the conformal algebra AC(1,2) for quasilinear second-order differential equations". Bukovinian Mathematical Journal. 2 no. 2-3.

Export

BibTex EndNote RIS