GENERIC formulation and small-angle limit for Kinetic wave equations

TL;DR

This paper reformulates kinetic wave equations within the GENERIC framework and derives a small-angle limit, revealing structural similarities to classical kinetic limits and demonstrating the GENERIC structure of the resulting system.

Contribution

It introduces a GENERIC formulation for three-wave and four-wave kinetic equations and formally derives a small-angle limit for the four-wave equation.

Findings

Established the GENERIC structure of the kinetic wave equations.

Derived a formal small-angle limit analogous to the grazing limit in kinetic theory.

Showed the limiting system also possesses a GENERIC structure.

Abstract

In this paper, we formulate the three-wave and four-wave kinetic equations into the GENERIC framework and formally derive a small-angle limit for the four-wave equation. This limit is akin to the well-known grazing limit from the kinetic Boltzmann equation to the kinetic Landau equation. We also show the GENERIC structure of the limiting system.