Optical-fluid dark line and X solitary waves in Kerr media

We consider the existence and propagation of nondi ractive and nondispersive spatiotemporal optical wavepackets in nonlinear Kerr media. We report analytically and con rm numerically the properties of spatiotemporal dark line solitary wave solutions of the (2+1)D nonlinear Schrödinger equation (NLSE). Dark lines represent holes of light on a continuous wave background. Moreover, we consider nontrivial web patterns generated under interactions of dark line solitary waves, which give birth to dark X solitary waves. These solitary waves are derived by exploiting the connection between the NLSE and a wellknown equation of hydrodynamics, namely the (2 + 1)D type II Kadomtsev-Petviashvili (KP-II) equation. This nding opens a novel path for the excitation and control of optical solitary waves, of hydrodynamic nature.