Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-11-28
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
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.
de Leur Johan van
Igonin Sergei
Manno Gianni
Trushkov V.
No associations
LandOfFree
Generalized Landau-Lifshitz systems and Lie algebras associated with higher genus curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized Landau-Lifshitz systems and Lie algebras associated with higher genus curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Landau-Lifshitz systems and Lie algebras associated with higher genus curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-139334