Self-consistent dynamics in the single wave model

A numerical study of self-consistent dynamics is presented in the context of the single-wave model (SWM). The SWM is a general mean-field model that describes the weakly nonlinear dynamics of marginally stable plasmas and fluids. Also, the SWM bears many similarities with models used to describe coupled oscillator systems. We construct integrable solutions of the SWM, and illustrate the concept of self-consistent resonant mixing by following numerically the evolution of perturbed integrable solutions. Using Fourier analysis we construct kinematic effective Hamiltonians.