On the complete integrability of the Raychaudhuri differential system in \(\mathbb {R}^4\) and of a CRNT model in \(\mathbb {R}^5\)
The Raychaudhuri equation is a four-parameter quadratic polynomial system of ordinary differential equations on \(\mathbb R^4\) that arises in the theory of general relativity. The authors prove that it is completely integrable, i.e., that it has three functionally linearly independent first integrals, and that they are of Darboux type. Moreover on a set of parameters of full Lebesgue measure the first integrals are rational. The second system studied is a five-parameter quadratic polynomial system of ordinary differential equations on \(\mathbb R^5\). It arises from an enzymatic mechanism in chemical reaction network theory. The authors show, among other things, that it has two linear first integrals, of which any other polynomial first integral is a polynomial function. They find all Darboux polynomials and exponential factors and show that the system is not Darboux integrable.
scientific article; zbMATH DE number 6891614
scientific article