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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We enlarge the spectral problem of a generalized D-Kaup-Newell (D-KN)spectral problem. Solving the enlarged zero-curvature equations, we produceintegrable couplings. A reduction of the spectral matrix leads to a secondintegrable coupling system. Next, bilinear forms that are symmetric,ad-invariant, and non-degenerate on the given non-semisimple matrix Lie algebraare computed to employ the variational identity. The variational identity isthen applied to the original enlarged spectral problem of a generalized D-KNhierarchy and the reduced problem. Hamiltonian structures are presented, aswell as a bi-Hamiltonian formulation of the reduced problem. Both hierarchieshave infinitely many commuting symmetries and conserved densities, i.e., areLiouville integrable.

Integrable couplings of a generalized D-Kaup-Newell hierarchy and their Hamiltonian structures