On the Complete Integrability of the Raychaudhuri Differential System in ℝ4 and of a CRNT Model in ℝ5
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
On the Complete Integrability of the Raychaudhuri Differential System in ℝ4 and of a CRNT Model in ℝ5Date
2018-04ISSN
1575-5460; 1662-3592Bibliographic citation
FERRAGUT, Antoni; VALLS, Claudia. On the Complete Integrability of the Raychaudhuri Differential System in ℝ4 and of a CRNT Model in ℝ5. Qualitative Theory of Dynamical Systems, 2018, vol. 17, no 1, p. 291-307.Type
info:eu-repo/semantics/articlePublisher version
https://link.springer.com/article/10.1007%2Fs12346-017-0230-7Version
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Abstract
We study the Darboux integrability of two differential systems with parameters: the Raychaudhuri equation (a relativistic model in ℝ4 ) and a chemical reaction model in ℝ5 . We prove that the first one is completely ... [+]
We study the Darboux integrability of two differential systems with parameters: the Raychaudhuri equation (a relativistic model in ℝ4 ) and a chemical reaction model in ℝ5 . We prove that the first one is completely integrable and that the first integrals are of Darboux type. This is the first four-dimensional realistic non-trivial model which is completely integrable with first integrals of Darboux type and for which for a full Lebesgue measure set of the values of the parameters the three linearly independent first integrals are rational. For the second one, we find all its Darboux polynomials and exponential factors and we prove that it is not Darboux integrable. [-]
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Qualitative Theory of Dynamical Systems, 2018, vol. 17, no 1Investigation project
Spanish Government: MTM2013-40998-P; Universitat Jaume I Grant: P1-1B2015-16; FCT - Fundacao para a Ciencia e a Tecnologia: PTDC/MAT/117106/2010; CAMGSDRights
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