Toroidal Lie algebras and Bogoyavlensky's 2+1-dimensional equation

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dc.creatorIkeda, T.
dc.creatorTakasaki, K.
dc.date2000-04-10
dc.date2000-09-05
dc.date.accessioned2026-07-07T05:32:46Z
dc.date.available2026-07-07T05:32:46Z
dc.descriptionWe introduce an extension of the \ell-reduced KP hierarchy, which we call the \ell-Bogoyavlensky hierarchy. Bogoyavlensky's 2+1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of \ell=2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl_\ell^{tor}. This reproduces essentially the same Hirota bilinear equations as those recently introduced by Billig and Iohara et al. We can further derive these Hirota bilinear equation from a Lax formalism of the hierarchy.This Lax formalism also enables us to construct a family of special solutions that generalize the breaking soliton solutions of Bogoyavlensky. These solutions contain the N-soliton solutions, which are usually constructed by use of vertex operators.
dc.descriptionLatex2e with amsmath,amssymb, 35 pages, no figures, (v2) typos corrected, added info on ref.[30] (v3) added a reference and some examples (v4) added some comments in subsection 4.4
dc.identifierhttps://arxiv.org/abs/nlin/0004015
dc.identifierhttp://arxiv.org/abs/nlin/0004015
dc.identifierInternat. Math. Res. Notices 2001, No. 7, 329-369
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79775
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleToroidal Lie algebras and Bogoyavlensky's 2+1-dimensional equation
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