On the Complete Integrability of the Raychaudhuri Differential System in R 4 and of a CRNT Model in R 5

  1. Ferragut, Antoni 1
  2. Valls, Claudia 2
  1. 1 Universitat Jaume I
    info

    Universitat Jaume I

    Castelló de la Plana, España

    ROR https://ror.org/02ws1xc11

  2. 2 Universidade de Lisboa
    info

    Universidade de Lisboa

    Lisboa, Portugal

    ROR https://ror.org/01c27hj86

Revue:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Année de publication: 2018

Volumen: 17

Número: 1

Pages: 291-307

Type: Article

DOI: 10.1007/S12346-017-0230-7 DIALNET GOOGLE SCHOLAR lock_openAccès ouvert editor

D'autres publications dans: Qualitative theory of dynamical systems

Résumé

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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