Onset of transverse instabilities of confined dark solitons

Abstract

We investigate propagating dark soliton solutions of the two-dimensional defocusing nonlinear Schrödinger / Gross-Pitaevskii (NLS/GP) equation that are transversely confined to propagate in an infinitely long channel. Families of single, vortex, and multi-lobed solitons are computed using a spectrally-accurate numerical scheme. The multi-lobed solitons are unstable to small transverse perturbations. However, the single-lobed solitons are stable if they are sufficiently confined along the transverse direction, which explains their effective one-dimensional dynamics. The emergence of a transverse modulational instability is characterized in terms of a spectral bifurcation. The critical confinement width for this bifurcation is found to coincide with the existence of a propagating vortex solution and the onset of a "snaking" instability in the dark soliton dynamics that, in turn, give rise to vortex or multi-vortex excitations. These results shed light on the superfluidic hydrodynamics of dispersive shock waves in Bose-Einstein condensates and nonlinear optics.

11 pages, 11 figures

References in corpus (7)

• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Dispersive shock waves and modulation theory
• Observation of Solitonic Vortices in Bose-Einstein Condensates
• Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier
• Solitons, solitonic vortices, and vortex rings in a confined Bose-Einstein condensate
• Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays
• Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids

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• Dynamics and stabilization of bright soliton stripes in the hyperbolic-dispersion nonlinear Schrödinger equation
• Shock Waves in a Superfluid with Higher-Order Dispersion
• Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates
• Transverse instabilities of stripe domains in magnetic thin films with perpendicular magnetic anisotropy
• Variational Approach to the Snake Instability of a Bose-Einstein Condensate Soliton
• Characterising arbitrary dark solitons in trapped one-dimensional Bose-Einstein condensates