Energy transfer model and large periodic boundary value problem for the quintic nonlinear Schrodinger equations

We study a dynamics and energy exchanges between a linear oscillator and a nonlinear interaction state for the one dimensional, quintic nonlinear Schrodinger equation. Grebert and Thomann proved that there exist solutions with initial data built on four Fourier modes, that confirms the conservative exchange of wave energy. Captured multi resonance in multiple Fourier modes, we simulate a similar energy exchange in long-period waves.