Dark Solitons: From 1D to 2D and 3D with Some Quantum Touches
In the present talk, we will revisit some principal excitations in self-repulsive Bose-Einstein condensates, namely dark solitons in single-component systems, and dark-bright solitons in multi-component systems. Upon introducing them and explaining their existence and stability properties in 1d, we will extend them both in the form of stripes and in that rings in two-dimensions, presenting an alternative (adiabatic-invariant based) formulation of their stability and excitations. We will explore their filamentary dynamics, as well as the states that emerge from their transverse (snaking) instability. Then, we will consider these structures even in three dimensions, in the form of planar, as well as spherical shell solitons and generalize our adiabatic invariant formulation there. Finally, time permitting, we will give some glimpses of how some of these dynamical features in 1d and 2d generalize in a multi-orbital, time-dependent quantum setting.