Propagation of acoustic black solitons in a bubbly liquid model incorporating thermal conduction at the bubble–liquid interface and liquid compressibility

The propagation of acoustic black solitons in a bubbly liquid model incorporating bubble–liquid interface thermal conduction and liquid compressibility is theoretically and numerically investigated, and the effects of nonlinearity, dispersion, and dissipation on their dynamic characteristics are analyzed. By applying the multiple-scale perturbation method, the lossy nonlinear Schrödinger (NLS) equation is derived, and analytical expressions for envelope acoustic black solitons are obtained. The non-negligible importance of thermal conduction is demonstrated: when it is neglected, a focusing NLS equation with a positive product of nonlinear and dispersion coefficients is derived, supporting only bright solitons; when it is included, a defocusing NLS equation with a negative product is obtained, supporting only acoustic black solitons. This transition in soliton type arises because thermal conduction modifies the dispersion relation and group velocity. The contributions of both thermal conduction and liquid compressibility to dissipation are also analyzed. Finally, the temperature- and amplitude-dependent propagation of lossy acoustic black solitons is investigated, confirming that the analytical solutions accurately capture their dynamic features in nonlinear, dispersive, and dissipative media.