On integrability of the Szekeres system. I. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Gierzkiewicz, Anna; Golda, Zdzisław A.
• Is Part Of: Journal of nonlinear mathematical physics. Volume 23:Issue 4(2016)
• Page Start: 494
• Page End: 506
• Publication Date: 2016-10-01
• Subjects: First integral -- Szekeres system -- Darboux polynomial -- Jacobi Last Multiplier -- Poincaré compactifi- cation; 37J35 -- 83C15 -- 83C20; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2016.1237199
• Languages: English
• ISSNs: 1402-9251

Abstract

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.