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

International audienceWe consider the generalized Benjamin-Ono equation,  regularized in the same manner that the  Benjamin-Bona-Mahony equation is found from the  Korteweg-de Vries equation  \cite{bbm}, namely the equation  $u_t + u_x +u^\rho u_x + H(u_{xt})=0,$ where $H$ is the Hilbert transform. In a second time, we consider the generalized Kadomtsev-Petviashvili-II equation,  also regularized, namely the equation   $u_t + u_x +u^\rho u_x - u_{xxt} +\partial_x^{-1}u_{yy} =0$. We are interested in  dispersive properties of these equations for small initial data. We  will show that, if the power $\rho$ of the nonlinearity is higher than $3$,  the respective solution of these equations tends to zero when time rises with a decay rate  of order close to  $\frac{1}{2}$

On the decay in time of solutions of some generalized regularized long waves equations