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

Periodic travelling waves are considered in the class of reduced Ostrovskyequations that describe low-frequency internal waves in the presence ofrotation. The reduced Ostrovsky equations with either quadratic or cubicnonlinearities can be transformed to integrable equations of the Klein--Gordontype by means of a change of coordinates. By using the conserved momentum andenergy as well as an additional conserved quantity due to integrability, weprove that small-amplitude periodic waves are orbitally stable with respect tosubharmonic perturbations, with period equal to an integer multiple of theperiod of the wave. The proof is based on construction of a Lyapunovfunctional, which is convex at the periodic wave and is conserved in the timeevolution. We also show numerically that convexity of the Lyapunov functionalholds for periodic waves of arbitrary amplitudes.

Orbital stability of periodic waves in the class of reduced Ostrovsky equations