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

In the present work we provide a characterization of the ground states of ahigher-dimensional quadratic-quartic model of the nonlinear Schr{\"o}dingerclass with a combination of a focusing biharmonic operator with either anisotropic or an anisotropic defocusing Laplacian operator (at the linear level)and power-law nonlinearity. Examining principally the prototypical example ofdimension $d=2$, we find that instability arises beyond a certain thresholdcoefficient of the Laplacian between the cubic and quintic cases, while allsolutions are stable for powers below the cubic. Above the quintic, and up to acritical nonlinearity exponent $p$, there exists a progressively narrowingrange of stable frequencies. Finally, above the critical $p$ all solutions areunstable. The picture is rather similar in the anisotropic case, with thedifference that even before the cubic case, the numerical computations suggestan interval of unstable frequencies. Our analysis generalizes the relevantobservations for arbitrary combinations of Laplacian prefactor $b$ andnonlinearity power $p$.

Mixed dispersion nonlinear Schr\"odinger equation in higher dimensions: theoretical analysis and numerical computations