Ultracold two-dimensional (2D) Bose gases exhibit behaviour that differs markedly from their three-dimensional counterparts, making them a sensitive setting for studying symmetry and interaction effects. In the idealized Gross-Pitaevskii equation (GPE), scale invariance gives rise to unique phenomena such as Townes solitons, 'strong' self-similar collapse, and interaction-independent breathing-mode frequencies in tightly trapped systems. However, realistic bosonic systems exhibit a strong quantum anomaly, namely, a breaking of scale invariance and, in consequence, the formation of universal droplets. It remains unclear whether a simple, unified theoretical framework exists to analyse these phenomena. To address that, we introduce a density-dependent coupling into the GPE, which successfully describes this behavior, while preserving a structure suitable for intuitive analytical and numerical exploration.

In this talk, I will discuss the unique properties of ultracold low-dimensional Bose gases, with a focus on the 2D attractive Bose gas. I will show our limitations in the mathematical description of those systems and how we can overcome them with the recently introduced generalized GPE. The talk will address new experimental opportunities and theoretical challenges.