Integrability of Dirac Reduced Bi-Hamiltonian Equations

Erratum to: Classical $${\mathcal {W}}$$ W -Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents

“…, 1) of m + s. (Note that for both hierarchies the number of fields is equal to m −1+2s = dim( g f g f 0 ).) For m = 2 this observation is proved in [DSKV14b].…”

“…Thus, in Sect. 2.5 of [DSKV14b] we proved that the n − 2-component YO hierarchy is obtained by Dirac reduction from the minimal sl n generalized Drinfeld-Sokolov hierarchy. As a result, we gave two compatible Poisson structures for the n − 2-component YO hierarchy, which we denoted by H 0 and H D 1 in Sect.…”

“…As a result, we gave two compatible Poisson structures for the n − 2-component YO hierarchy, which we denoted by H 0 and H D 1 in Sect. 2.5 of [DSKV14b].…”

Introduction to Vertex Algebras, Poisson Vertex Algebras, and Integrable Hamiltonian PDE

“…This approach establishes integrability of the NLS equation, see [DSKV14a] for details. For other approaches see [TF86] and [DSK13].…”