2 0 A ug 2 00 0 Toroidal Lie algebras and Bogoyavlensky ’ s 2 + 1-dimensional equation

Abstract

We introduce an extension of the l-reduced KP hierarchy, which we call the lBogoyavlensky hierarchy. Bogoyavlensky’s 2 + 1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of l = 2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl l . This reproduces… (More)

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