Solitonic vortices and the fundamental modes of the snake instability: Possibility of observation in the gaseous Bose-Einstein condensate

The connection between quantized vortices and dark solitons in a waveguidelike trap geometry is explored in the framework of the nonlinear Schrodinger equation. Variation of the transverse confinement leads from the quasi-one-dimensional (1D) regime, where solitons are stable, to 2D (or 3D) confinement, where soliton stripes are subject to a transverse modulational instability known as the snake instability. We present numerical evidence of a regime of intermediate confinement where solitons decay into single, deformed vortices with solitonic properties rather than vortex pairs as associated with the snake metaphor. Further relaxing the transverse confinement leads to the production of two and then three vortices, which correlates perfectly with a Bogoliubov stability analysis. The decay of a stationary dark soliton (or, planar node) into a single solitonic vortex is predicted to be experimentally observable in a 3D harmonically confined dilute-gas Bose-Einstein condensate.