Structure of caustics shortly after the shell-crossing for three-sine-wave initial conditions: comparison of LPT predictions using ballistic approximation with Vlasov runs. The top six, middle six, and bottom two panels respectively correspond to Q1D-3SIN, ANI-3SIN, and SYM-3SIN. In each group of six panels, the top and bottom lines correspond to Lagrangian and Eulerian spaces, and the intersection of the caustic surfaces with the plane are q_x = 0, q_y = 0, and q_z = 0, respectively, for the first, second, and third column of each group. In the bottom group of two panels, the left and right panels correspond respectively to Lagrangian and Eulerian space and only show the intersection of the caustic surface network with the plane q_z = 0 due to the symmetry of the system.