Radial profiles and their logarithmic slopes for the two-sine-wave initial conditions at the shell-crossing time. As indicated in top-left panel, LPT predictions are given by solid lines of various colours and Vlasov simulations results are represented by red dots. From left to right, the initial conditions are given by Q1D-2SIN (ϵ_2D = 1/6), ANI-2SIN (ϵ_2D = 2/3), and SYM-2SIN (ϵ_2D = 1), respectively. From top to bottom, we present the radial profiles of the normalised density , the velocity dispersion υ², the radial velocity dispersion , the infall velocity -υ_r, and the pseudo phase-space density Q(r), respectively. We note that when plotting the logarithmic slopes in Vlasov simulations, we used the Savitzky-Golay filter implemented in savgol_filter of SciPy (Virtanen et al. 2020) to smooth the data for presentation purposes. In the logarithmic slope panels, the horizontal dashed lines correspond to the theoretical predictions at the small radii of Appendix D, as listed in Table 2.