On the complete integrability of the Raychaudhuri differential system in R^4 and of a CRNT model in R^5
Ferragut Amengual, Antoni Manel (Universitat Jaume I. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)

Date:	2017
Abstract:	WestudytheDarbouxintegrabilityoftwodifferentialsystemswithparam- eters: 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 inte- grals 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 indepen- dent 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.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P
Note:	Agraïments: A. Ferragut is partially supported by the Universitat Jaume I Grant P1-1B2015-16. C.Valls is supported by Portuguese National Funds through FCT - Fundação para a Ciência e a Tecnologia within the Project PTDC/MAT/117106/2010 and by CAMGSD.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Chemical reaction network ; Darboux integrability ; Darboux polynomial ; Exponential factor ; Raychaudhuri equation
Published in:	Qualitative theory of dynamical systems, 2017 , ISSN 1662-3592

DOI: 10.1007/s12346-017-0230-7

Postprint 16 p, 266.5 KB

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