Solitary waves in a quantum droplet-bearing system

We unravel the existence and stability properties of dark soliton solutions as they extend from regime trapped quantum droplets towards Thomas-Fermi limit in homonuclear symmetric Bose mixtures. Leveraging a phase-plane analysis, we identify regimes different types subsequently examine possibility black gray solitons kink-type structures this system. Moreover, employ Landau dynamics approach to extract an analytical estimate oscillation frequency single relevant extended Gross--Pitaevskii model. Within framework, also find that immersed droplet is stable, while multisoliton configurations exhibit parametric windows oscillatory instabilities. Our results pave way for studying dynamical features nonlinear excitations environment contemporary experimental settings.