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 derive the $2$d Zakharov-Mikhailov action from $4$d Chern-Simons theory.This $2$d action is known to produce as equations of motion the flatnesscondition of a large class of Lax connections of Zakharov-Shabat type, whichincludes an ultralocal variant of the principal chiral model as a special case.At the $2$d level, we determine for the first time the covariant Poissonbracket $r$-matrix structure of the Zakharov-Shabat Lax connection, which is ofrational type. The flatness condition is then derived as a covariant Hamiltonequation. We obtain a remarkable formula for the covariant Hamiltonian in termof the Lax connection which is the covariant analogue of the well-known formula"$H=Tr L^2$".

On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection