English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We put the Adler-Gelfand-Dickey approach to classical W-algebras in theframework of Poisson vertex algebras. We show how to recover the bi-Poissonstructure of the KP hierarchy, together with its generalizations and reductionto the N-th KdV hierarchy, using the formal distribution calculus and thelambda-bracket formalism. We apply the Lenard-Magri scheme to proveintegrability of the corresponding hierarchies. We also give a simple proof ofa theorem of Kupershmidt and Wilson in this framework. Based on this approach,we generalize all these results to the matrix case. In particular, we find(non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdVhierarchies, and we prove integrability of the N-th matrix KdV hierarchy.

Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras