Laboratoire Emile Picard, U.M.R. C.N.R.S. 5580, Département de Mathématiques, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France ; Université Libanaise, Beyrouth, BP 13.5292 Chouran, Lebanon
Abstract:
Using the Spencer-Goldschmidt version of the Cartan-Kähler theorem, we give conditions for (local) existence of conservation laws for analytical quasi-linear systems of two independent variables. This result is applied to characterize the recursion operator (in the sense of Magri) of completely integrable systems.