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

In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov--Kuznetsov equation on $\mathbb{R}\times \mathbb{T}_L$ and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction is based on the graph transform approach by Nakanishi and Schlag. Applying the bilinear estimate on Fourier restriction spaces by Molinet and Pilod and modifying the mobile distance by Nakanishi and Schlag, we construct a contraction map on the graph space.

Center stable manifolds around line solitary waves of the Zakharov–Kuznetsov equation with critical speed