Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive
spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media.
Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave
solutions of the ð2 þ 1ÞD nonlinear Schrödinger equation. Dark lumps represent multidimensional holes
of light on a continuous wave background.We analytically derive the dark lumps from the hydrodynamic
exact soliton solutions of the ð2 þ 1ÞD shallow water Kadomtsev-Petviashvili model, inheriting their
complex interaction properties. This finding opens a novel path for the excitation and control of optical
spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave
phenomena.