Generalized Landau-Lifshitz systems and Lie algebras associated with higher genus curves
| dc.creator | Igonin, S. | |
| dc.creator | van de Leur, J. | |
| dc.creator | Manno, G. | |
| dc.creator | Trushkov, V. | |
| dc.date | 2008-11-28 | |
| dc.date.accessioned | 2026-07-07T12:06:20Z | |
| dc.date.available | 2026-07-07T12:06:20Z | |
| dc.description | The 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.identifier | https://arxiv.org/abs/0811.4669 | |
| dc.identifier | http://arxiv.org/abs/0811.4669 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208623 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | Rings and Algebras | |
| dc.title | Generalized Landau-Lifshitz systems and Lie algebras associated with higher genus curves | |
| dc.type | text |