Volume 23, Issue 4, September 2016, Pages 494 - 506
On integrability of the Szekeres system. I
Authors
Anna Gierzkiewicz
Department of Applied Mathematics, University of Agriculture in Kraków, ul. Balicka 253c, 30–198 Kraków, Poland
Astronomical Observatory of the Jagiellonian University ul. Orla 171, 30–244 Kraków, Poland,anna.gierzkiewicz@ur.krakow.pl
Zdzisław A. Golda
Astronomical Observatory of the Jagiellonian University ul. Orla 171, 30–244 Kraków, Poland,zdzislaw.golda@uj.edu.pl
Received 24 March 2016, Accepted 25 July 2016, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1237199How to use a DOI?
- Keywords
- First integral; Szekeres system; Darboux polynomial; Jacobi Last Multiplier; Poincaré compactifi- cation
- Abstract
The Szekeres system is a four-dimensional system of first-order ordinary differential equations with nonlinear but polynomial (quadratic) right-hand side. It can be derived as a special case of the Einstein equations, related to inhomogeneous and nonsymmetrical evolving spacetime. The paper shows how to solve it and find its three global independent first integrals via Darboux polynomials and Jacobi’s last multiplier method. Thus the Szekeres system is completely integrable. Its two-dimensional subsystem is also investigated: we present its solutions explicitly and discuss its behaviour at infinity.
- Copyright
- © 2016 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Anna Gierzkiewicz AU - Zdzisław A. Golda PY - 2021 DA - 2021/01/06 TI - On integrability of the Szekeres system. I JO - Journal of Nonlinear Mathematical Physics SP - 494 EP - 506 VL - 23 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1237199 DO - 10.1080/14029251.2016.1237199 ID - Gierzkiewicz2021 ER -