# A reaction network approach to the theory of acoustic wave turbulence

## TL;DR

This paper introduces a novel chemical reaction network framework to analyze the long-term behavior of acoustic wave turbulence, demonstrating exponential convergence to equilibrium and effects of resonance broadening.

## Contribution

It reformulates the wave kinetic equation as a chemical reaction network and applies dynamical systems techniques to study its long-term behavior.

## Key findings

- Solution converges exponentially to equilibrium.
- Resonance broadening can cause solutions to diverge.
- New approach links wave turbulence with chemical reaction dynamics.

## Abstract

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.