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 consider the effect of real spectral singularities on the long time behavior of the solutions of the focusing Nonlinear Schroedinger equation. We find that for each spectral singularity λ′ ∈ℝ, such an effect is limited to the region of the (x,t)-plane in which λ′ is close to the point of stationary phase<img src="/fulltext-image.asp?format=htmlnonpaginated&src=P242750Q549N2MR4_html\220_2005_Article_BF02099716_TeX2GIFIE1.gif" border="0" alt="$$\lambda _0  = \tfrac{{ - x}}{{4t}}$$" /> (the phase here being defined in a standard way by, say, the evolution of the Jost functions). In that region, the solution performs decaying oscillations of the same form as in the other regions, but with different parameters. The order of decay is<img src="/fulltext-image.asp?format=htmlnonpaginated&src=P242750Q549N2MR4_html\220_2005_Article_BF02099716_TeX2GIFIE2.gif" border="0" alt="$$O\left( {\left( {\tfrac{{\log t}}{t}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right)$$" />.

Long time behavior for the focusing nonlinear schroedinger equation with real spectral singularities