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 use the inverse scattering transform and a diffusion approximation limittheorem to study the stability of soliton components of the solution of thenonlinear Schr\"{o}dinger and Korteweg-de Vries equations under randomperturbations of the initial conditions: for a wide class of rapidlyoscillating random perturbations this problem reduces to the study of acanonical system of stochastic differential equations which depends only on theintegrated covariance of the perturbation. We finally study the problem whenthe perturbation is weak, which allows us to analyze the stability of solitonsquantitatively.

Stability of solitons under rapidly oscillating random perturbations of the initial conditions