  The isotropic 4-wave kinetic equation is considered in its weak formulation
using model (simplified) homogeneous kernels. Existence and uniqueness of
solutions is proven in a particular setting where the kernels have a rate of
growth at most linear. We also consider finite stochastic particle systems
undergoing instantaneous coagulation- fragmentation phenomena and give
conditions in which this system approximates the solution of the equation
(mean-field limit).
