Integrable Systems, Spectral Curves and Representation Theory

Volume 3, Issue 1, Article 1 - 2017

Authors: A. Lesfari

Copyright © 2017 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

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 Adler-Kostant-Symes 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 algebraic-geometric 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.

How To Cite This Article

@article{2017, doi = {10.31559/glm2016.3.1.1}, url = {https://doi.org/10.31559%2Fglm2016.3.1.1}, year = 2017, month = {aug}, publisher = {Refaad for Studies and Research}, volume = {3}, number = {1}, title = {Integrable Systems, Spectral Curves and Representation Theory}, journal = {General Letters in Mathematics} }
Integrable Systems, Spectral Curves and Representation Theory. (2017). General Letters in Mathematics, 3(1). doi:10.31559/glm2016.3.1.1
[1]“Integrable Systems, Spectral Curves and Representation Theory,” General Letters in Mathematics, vol. 3, no. 1, Aug. 2017.
“Integrable Systems, Spectral Curves and Representation Theory.” General Letters in Mathematics 3, no. 1 (August 1, 2017). doi:10.31559/glm2016.3.1.1.