Stability of stationary solutions in acoustic wave turbulence

We study the stability of steady-state solutions of the Wave Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both two- and three-dimensional equilibrium Rayleigh-Jeans and nonequilibrium Kolmogorov-Zakharov solutions. In particular, we show that the stability of these solutions is ensured by different mechanisms.