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 build Gaussian wave packets for the linear Schr\"odinger equation and itsfinite difference space semi-discretization and illustrate the lack of uniformdispersive properties of the numerical solutions as established in Ignat,Zuazua, Numerical dispersive schemes for the nonlinear Schr\"odinger equation,SIAM. J. Numer. Anal., 47(2) (2009), 1366-1390. It is by now well known thatbigrid algorithms provide filtering mechanisms allowing to recover theuniformity of the dispersive properties as the mesh size goes to zero. Weanalyze and illustrate numerically how these high frequency wave packets splitand propagate under these bigrid filtering mechanisms, depending on how thefine grid/coarse grid filtering is implemented.

High frequency wave packets for the Schr\"odinger equation and its numerical approximations