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Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations

par Goriely, Alain
Référence Journal of mathematical physics, 37, 4, page (1871-1893)
Publication Publié, 1996-04

Article révisé par les pairs

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Résumé :

The integrability of systems of ordinary differential equations with polynomial vector fields is investigated by using the singularity analysis methods. Three types of results are obtained. First, a general relationship between the degrees of first integrals and the so-called Kowalevskaya exponents is derived. Second, it is shown that all solutions of algebraically integrable systems can be expanded in Puiseux series. Third, a new method to study partially integrable systems is studied. These different aspects allow us to study algorithmically the integrability, partial integrability, and nonintegrability of differential systems. © 1996 American Institute of Physics.