Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation
Abstract
We describe deformations of the classical principal chiral model and the $(1+1)$-dimensional Gaudin model related to the Lie group $\mathrm{GL}_N$. The deformations are generated by $R$-matrices satisfying the associative Yang-Baxter equation. Using the coefficients of the expansion for these $R$-matrices we derive equations of motion based on a certain ansatz for $U$-$V$ pair satisfying the Zakharov-Shabat equation. Another deformation comes from the twist function, which we identify with the cocentral charge in the affine Higgs bundle underlying the Hitchin approach to $2d$ integrable models.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Advanced Algebra and Geometry
Advanced Topics in Algebra
Publication details
- Journal / source
- Izvestiya Mathematics
- Volume
- 90
- Issue
- 1
- Pages
- 109–143
- Publication date
- 1 January 2026
- Language
- EN