Bosonizations of sl₂ and Integrable Hierarchies - Bakalov, B.; Fleisher, D. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
We construct embeddings of sl₂ in lattice vertex algebras by composing the Wakimoto realization with the Friedan-Martinec-Shenker bosonization. The Kac-Wakimoto hierarchy then gives rise to two new hierarchies of integrable, non-autonomous, non-linear partial differential equations. A new feature of our construction is that it works for any value of the central element of sl₂; that is, the level becomes a parameter in the equations.