Coherent nonlinear waves in a two-dimensional droplet bearing model

Quantum droplets are self-bound many-body states arising in binary bosonic mixtures due to the balance of mean-field attraction and repulsive quantum fluctuations. Their characteristics can be well-captured within the extended Gross-Pitaevskii formalism. We report on the existence, stability and dynamics of solitary wave excitations and bubbles embedded in two-dimensional droplet environments. The excitation spectra of such configurations are analyzed within the Bogoliubov-de-Gennes framework exposing destabilizations thereof. The existence of these configurations is corroborated through an effective potential picture and their stability is further testified via a variational approximation which gives access to the respective dispersion relation for arbitrary velocities and chemical potentials.