Transverse dynamics of vector solitons in defocusing nonlocal media

The transverse instability of line solitons of a multicomponent nonlocal defocusing nonlinear Schrödinger (NLS) system is utilized to construct lump and vortex-like structures in 2D nonlocal media, such as nematic liquid crystals. These line solitons are found by means of a perturbation expansion technique, which reduces the nonintegrable vector NLS model to a completely integrable scalar one, namely to a Kadomtsev–Petviashvili equation. It is shown that dark or antidark soliton stripes, as well as dark lumps, are possible depending on the strength of nonlocality: dark (antidark) solitons are formed for weaker (stronger) nonlocality, relatively to a threshold that is analytically determined in terms of the parameters of the system and the continuous-wave amplitude. Direct numerical simulations are used to show that dark lump-like- and vortex-like-structures can spontaneously be formed as a result of the transverse instability of the dark soliton stripes.