Higher dimensional generalization of the Benjamin‐Ono equation: 2D case

We consider a higher-dimensional version of the Benjamin-Ono (HBO) equation in 2D setting: , which is -critical, and investigate properties solutions both analytically numerically. For generalized (fractional gKdV) after deriving Pohozaev identities, we obtain nonexistence conditions for solitary wave solutions, then prove uniform bounds energy space or conditional global existence, radiation region, specific wedge negative -direction. introduce our numerical approach general context, apply it to ground state solution critical HBO equation, show that its mass threshold versus finite time existing typical focusing (mass-)critical dispersive equations. also observe globally tend disperse completely into this nonlocal equation. The blow-up travel positive -direction with rescaled profile while radiating oscillations radiative wedge. conclude examples different interactions two including weak strong interactions.