We describe deformations of the classical principal chiral model and the (1+1) -dimensional Gaudin model related to the Lie group GLN. 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.
Domanevsky et al. (Thu,) studied this question.