1999/02/18 by Boris Feigin, Feigin, Boris, Edward Frenkel +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Rings, Modules, and Algebras #hep-th #math.QA #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.math/9902103
36 pages, Latex2e
openalex publication_date 1999/02/18 · arxiv created 2001/03/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our earlier papers we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV) hierarchies. In this paper we apply our approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and its generalizations. In particular, we show that the free field (Wakimoto) realization of an affine algebra naturally appears in the context of the generalized AKNS hierarchies. This is analogous to the appearance of the free field (quantum Miura) realization of a W-algebra in the context of the generalized KdV equations. As an application, we give here a new proof of the existence of the Wakimoto realization.