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 prove a threshold phenomenon for the existence/non-existence of energyminimizing solitary solutions of the diffraction management equation forstrictly positive and zero average diffraction. Our methods allow for a largeclass of nonlinearities, they are, for example, allowed to change sign, and theweakest possible condition, it only has to be locally integrable, on the localdiffraction profile. The solutions are found as minimizers of a nonlinear andnonlocal variational problem which is translation invariant. There exists acritical threshold ?cr such that minimizers for this variational problem existif their power is bigger than ?cr and no minimizers exist with power less thanthe critical threshold. We also give simple criteria for the finiteness andstrict positivity of the critical threshold. Our proof of existence ofminimizers is rather direct and avoids the use of Lions' concentrationcompactness argument.  Furthermore, we give precise quantitative lower bounds on the exponentialdecay rate of the diffraction management solitons, which confirm the physicalheuristic prediction for the asymptotic decay rate. Moreover, for ground statesolutions, these bounds give a quantitative lower bound for the divergence ofthe exponential decay rate in the limit of vanishing average diffraction. Forzero average diffraction, we prove quantitative bounds which show that thesolitons decay much faster than exponentially. Our results considerably extendand strengthen the results of [15] and [16].

Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities