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Transactions of the American Mathematical Society

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Existence of Conservation Laws
and characterization of recursion operators
for completely integrable systems


Authors: Joseph Grifone and Mohamad Mehdi
Journal: Trans. Amer. Math. Soc. 349 (1997), 4609-4633
MSC (1991): Primary 35G20, 35N10; Secondary 58F07, 58G30.
DOI: https://doi.org/10.1090/S0002-9947-97-01974-0
MathSciNet review: 1432200
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Joseph Grifone
Affiliation: 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
Email: grifone@picard.ups-tlse.fr

Mohamad Mehdi
Affiliation: Université Libanaise, Beyrouth, BP 13.5292 Chouran, Lebanon
Email: lusc1@lara.cnrs.edu.lb

DOI: https://doi.org/10.1090/S0002-9947-97-01974-0
Keywords: Quasi-linear partial differential equations, conservation laws, completely integrable systems, overdetermined system of partial differential equations, Cartan-K\"ahler theorem, Poisson-Nijenhuis manifolds
Received by editor(s): November 28, 1994
Received by editor(s) in revised form: April 3, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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