Refaad for Studies, Research and Developement
Integrable Systems, Spectral Curves and Representation Theory
25199269 (Print)
25199277 (Online)
Volume 3
Issue 1
2017

0
Integrable Systems, Spectral Curves and Representation Theory
1
24
English
A. LesfariDepartment of Mathematics, Faculty of Sciences, University of Choua¨ıb Doukkali, B.P. 20, El Jadida, Moroccolesfariahmed@yahoo.fr
The aim of this paper is to present an overview of the active area via the spectral linearization method for solving integrable systems. New examples of integrable systems, which have been discovered, are based on the so called Lax representation of the equations of motion. Through the AdlerKostantSymes construction, however, we can produce Hamiltonian systems on coadjoint orbits in the dual space to a Lie algebra whose equations of motion take the Lax form. We outline an algebraicgeometric interpretation of the ﬂows of these systems, which are shown to describe linear motion on a complex torus. These methods are exempliﬁed by several problems of integrable systems of relevance in mathematical physics.
Integrable systems; Jacobian varieties; spectral curves
http://www.refaad.com/views/GLM/311.html
http://www.refaad.com/Files/GLM/GLM311.pdf