Traveling Bubbles and Vortex Pairs within Symmetric 2D Quantum Droplets

TL;DR

This paper explores stable and unstable traveling wave solutions, including bubbles and vortex pairs, in symmetric 2D quantum droplets, revealing distinct regimes based on velocity and providing analytic insights.

Contribution

It introduces a comprehensive analysis of traveling bubbles and vortex pairs in 2D quantum droplets, including classification by velocity and unstable configurations with analytic approximations.

Findings

Identification of three velocity-based regimes with distinct vortex structures

Analytic approximations for different solution regimes

Extension to unstable vortex-antivortex pairs and arrays

Abstract

We disclose a class of stable nonlinear traveling waves moving at specific constant velocities within symmetric two-dimensional quantum droplets. We present a comprehensive analysis of these traveling bubbles and identify three qualitatively distinct regions within the one-parameter family of solutions, classified by velocity: (i) well-separated phase singularities at low velocity, (ii) singularities within the same density dip at intermediate velocity, and (iii) rarefaction pulses without singularities at higher (subsonic) velocities. Then, we generalize the discussion to unstable cases, incorporating higher order vortex-antivortex pairs and arrays of vortices that move cohesively with a common velocity within the fluid. In all cases, we provide analytic approximations that aid the understanding of the results in different regimes.