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We study the propagation of the two sound modes in two-dimensional Bose gasesacross the Berezinksii-Kosterlitz-Thouless (BKT) transition usingclassical-field dynamics, which is motivated by recent measurements ofChristodoulou et al. Nature 594, 191 (2021). Based on the dynamic structurefactor, we identify the two sound modes as the Bogoliubov (B) and thenon-Bogoliubov (NB) sound mode below the transition, and as the diffusive andthe normal sound mode above the transition. The NB sound mode velocity ishigher than the B sound mode velocity, which we refer to as the weak-couplingregime of the sound modes. We excite the sound modes by driving the system asin the experiment and by perturbing the density with a step-pulse perturbation,as a secondary comparison. The driven response depends on the driving strengthand results in higher velocities for the B sound mode at high temperatures nearthe transition, compared to the sound results of the dynamic structure factorand step-pulse excitation. We show that the higher mode velocity has a weaktemperature dependence across the transition, which is consistent with theexperimental observation.

First and second sound in a dilute Bose gas across the BKT transition