  We propose a new approach to study the long time dynamics of the wave kinetic
equation in the statistical description of acoustic turbulence. The approach is
based on rewriting the discrete version of the wave kinetic equation in the
form of a chemical reaction network, then employing techniques used to study
the Global Attractor Conjecture to investigate the long time dynamics of the
newly obtained chemical system. We show that the solution of the chemical
system converges to an equilibrium exponentially in time. In addition, a
resonance broadening modification of the acoustic wave kinetic equation is also
studied with the same technique. For the near-resonance equation, if the
resonance broadening frequency is larger than a threshold, the solution of the
system goes to infinity as time evolves.
