Two-dimensional dark soliton in the nonlinear Schroedinger equation
  Two-dimensional gray solitons to the nonlinear Schroedinger equation are numerically created by two processes to show its robustness. One is transverse instability of a one-dimensional gray soliton, and another is a pair annihilation of a vortex and an antivortex. The two-dimensional dark solitons are anisotropic and propagate in a certain direction. The two-dimensional dark soliton is stable against the head-on collision. The effective mass of the two-dimensional dark soliton is evaluated from the motion in a harmonic potential. 
Hidetsugu Sakaguchi and Tomoko Higashiuchi