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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study a class of 1+1 quadratically nonlinear water wave equations thatcombines the linear dispersion of the Korteweg-deVries (KdV) equation with thenonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet stillpreserves integrability via the inverse scattering transform (IST) method.  This IST-integrable class of equations contains both the KdV equation and theCH equation as limiting cases. It arises as the compatibility condition for asecond order isospectral eigenvalue problem and a first order equation for theevolution of its eigenfunctions. This integrable equation is shown to be ashallow water wave equation derived by asymptotic expansion at one order higherapproximation than KdV. We compare its traveling wave solutions to KdVsolitons.Comment: 4 pages, no figure

An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion