  A new dispersion equation is obtained for a non-equilibrium medium with an
exponential relaxation model of a vibrationally excited gas. We have researched
the dependencies of the pump source and the heat removal on the medium
thermodynamic parameters. The boundaries of sound waves stability regions in a
non-equilibrium gas have been determined. The nonlinear stage of sound waves
instability development in a vibrationally excited gas has been investigated
within CSPH-TVD and MUSCL numerical schemes using parallel technologies
OpenMP-CUDA. We have obtained a good agreement of numerical simulation results
with the linear perturbations dynamics at the initial stage of the sound waves
growth caused by instability. At the nonlinear stage, the sound waves amplitude
reaches the maximum value that leads to the formation of shock waves system.
