  In this work, we present the study of the stationary structures and the
breathing mode behavior of a two-dimensional self-bound binary Bose droplet. We
employ an analytical approach using a variational ansatz with a super-Gaussian
trial order parameter and compare it with the numerical solutions of the
extended Gross-Pitaevskii equation. We find that the super-Gaussian is superior
to the often used Gaussian ansatz in describing the stationary and dynamical
properties of the system. We find that for sufficiently large non-rotating
droplets the breathing mode is energetically favourable compared to the
self-evaporating process. For small self-bound systems our results differ based
on the ansatz. Inducing angular momentum by imprinting multiply quantized
vortices at the droplet center, this preference for the breathing mode persists
independent of the norm.
