Generalized Landau-Lifshitz systems and Lie algebras associated with higher genus curves

dc.creatorIgonin, S.
dc.creatorvan de Leur, J.
dc.creatorManno, G.
dc.creatorTrushkov, V.
dc.date2008-11-28
dc.date.accessioned2026-07-07T12:06:20Z
dc.date.available2026-07-07T12:06:20Z
dc.descriptionThe Wahlquist-Estabrook prolongation method allows to obtain for some PDEs a Lie algebra that is responsible for Lax pairs and Backlund transformations of certain type. We study the Wahlquist-Estabrook algebra of the n-dimensional generalization of the Landau-Lifshitz equation and construct an epimorphism from this algebra onto an infinite-dimensional quasigraded Lie algebra L(n) of certain matrix-valued functions on an algebraic curve of genus 1+(n-3)2^{n-2}. For n=3,4,5 we prove that the Wahlquist-Estabrook algebra is isomorphic to the direct sum of L(n) and a 2-dimensional abelian Lie algebra. Using these results, for any n a new family of Miura type transformations (differential substitutions) parametrized by points of the above mentioned curve is constructed. As a by-product, we obtain a representation of L(n) in terms of a finite number of generators and relations, which may be of independent interest.
dc.identifierhttps://arxiv.org/abs/0811.4669
dc.identifierhttp://arxiv.org/abs/0811.4669
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208623
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.subjectRings and Algebras
dc.titleGeneralized Landau-Lifshitz systems and Lie algebras associated with higher genus curves
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