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

Based on the gradient-holonomic algorithm we analyze the integrabilityproperty of the generalized hydrodynamical Riemann type equation$%D_{t}^{N}u=0$ for arbitrary $N\in \mathbb{Z}_{+}.$ The infinite hierarchiesof polynomial and non-polynomial conservation laws, both dispersive anddispersionless are constructed. Special attention is paid to the cases $%N=2,3$and N=4 for which the conservation laws, Lax type representations andbi-Hamiltonian structures are analyzed in detail. We also show that the caseN=2 is equivalent to a generalized Hunter-Saxton dynamical system, whoseintegrability follows from the results obtained. As a byproduct of our analysiswe demonstrate a new set of non-polynomial conservation laws for the relatedHunter-Saxton equation.

The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations