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

We consider space-periodic evolutionary and travelling-wave solutions to theregularised long-wave equation (RLWE) with damping and forcing. We establishexistence, uniqueness and smoothness of the evolutionary solutions for smoothinitial conditions, and global in time spatial analyticity of such solutionsfor analytical initial conditions. The width of the analyticity strip decays atmost polynomially. We prove existence of travelling-wave solutions anduniqueness of travelling waves of a sufficiently small norm. The importance ofdamping is demonstrated by showing that the problem of finding travelling-wavesolutions to the undamped RLWE is not well-posed. Finally, we demonstrate theasymptotic convergence of the power series expansion of travelling waves for aweak forcing.

Existence, uniqueness and analyticity of space-periodic solutions to the regularised long-wave equation