Two-dimensional dark soliton in the nonlinear Schrödinger equation

Two-dimensional gray solitons to the nonlinear Schrödinger 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.