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

Two-dimensional periodic surface waves propagating under the combinedinfluence of gravity and surface tension on water of finite depth areconsidered. Within the framework of small-amplitude waves, we find the exactsolutions of the nonlinear differential equation system which describes theparticle motion in the considered case, and we describe the possible particletrajectories. The required computations involve elliptic integrals of the firstkind, the Legendre normal form and a solvable Abel differential equation of thesecond kind. Some graphs of the results are included.

Small-amplitude capillary-gravity water waves: exact solutions and particle motion beneath such waves