TL;DR
This paper investigates integrable systems with Lax pairs featuring a spectral parameter and two poles in their R-matrix, revealing their interpretation as motions on a twisted loop algebra.
Contribution
It provides a solution to the classical Yang-Baxter equation for R-matrices with two poles and interprets these systems within the framework of twisted loop algebras.
Findings
R-matrices with two poles satisfy the classical Yang-Baxter equation
Integrable systems with such R-matrices correspond to motions on twisted loop algebras
The approach unifies certain classes of integrable models
Abstract
We study integrable dynamical systems described by a Lax pair involving a spectral parameter. By solving the classical Yang-Baxter equation when the R-matrix has two poles we show that they can be interpreted as natural motions on a twisted loop algebra.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Topics in Algebra