Sur la "solution analytique ge'ne'rale" d'une e'quation diffe'rentielle chaotique du troisie`me ordre
arXiv:nlin/0302056
Abstract
Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and Sivashinsky, which is generically chaotic and presents a high physical interest, we review various methods, all based on the structure of singularities, allowing us to characterize the analytic solution which depends on the largest possible number of constants of integration.
French. LaTex 2e. IRMA Lectures in Mathematics and Theoretical Physics (de Gruyter, Berlin, to appear in 2003)