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/

Zendy Plus

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

Zendy Tools

Zendy Open

We review recent results on global wellposedness and long-time behavior ofsmooth solutions to the derivative nonlinear Schr\"{o}dinger (DNLS) equation.Using the integrable character of DNLS, we show how the inverse scatteringtools and the method of Zhou for treating spectral singularities lead to globalwellposedness for general initial conditions in the weighted Sobolev space$H^{2,2}(\mathbb{R})$. For generic initial data that can support brightsolitons but exclude spectral singularities, we prove the soliton resolutionconjecture: the solution is asymptotic, at large times, to a sum of localizedsolitons and a dispersive component, Our results also show that solitonsolutions of DNLS are asymptotically stable.

The Derivative Nonlinear Schr\"{o}dinger Equation: Global Well-Posedness and Soliton Resolution