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Integrable discretizations of the KdV equation

Affiliation:	1. Steklov Mathematical Institute, Moscow, USSR;2. Institute of Theoretical Physics, University of Turku, Turku, Finland;1. Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, H-6720 Szeged, Hungary;2. Department of Theoretical Physics, WIGNER RCP, RMKI, H-1525 Budapest, P.O.B. 49, Hungary;1. Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, India;2. Physics Department, McGill University, 3600 University St, Montréal, QC H3A 2T8, Canada

Abstract:	Several dynamical systems are constructed having Lax representations with a spectral parameter and turning into the KdV equation in a continuous limit. A new hamiltonian integro-differential equation is derived having a Lax representation and an infinite set of conserved quantities. Integrable Lie algebraic generalizations of the Volterra system are pointed out.

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