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Existence of Conservation Laws and characterization of recursion operators for completely integrable systems |
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| Authors: | Joseph Grifone Mohamad Mehdi |
| Institution: | 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. |
| Keywords: | Quasi-linear partial differential equations conservation laws completely integrable systems overdetermined system of partial differential equations Cartan-K\"ahler theorem Poisson-Nijenhuis manifolds |
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