Field amplitudes of a particle-gas shear wave as a function of time. In this case, the system has a dimensionless stopping time of ﹩{\tau }_{s}=1﹩ and a solid-to-gas density ratio of ﹩{\epsilon }_{0}=1﹩, and its initial conditions are described in Section 4.1. The solid lines are the analytical solutions obtained from integrating Equations (45), while the circles are the measurements from each and every time step of the simulation data obtained by our algorithm. The top panel shows the velocity and density fields of the gas, while the bottom panel shows those of the particles.