On integrability of the Szekeres system. I. Issue 4 (1st October 2016) - Gierzkiewicz, Anna; Golda, Zdzisław A.
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.