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

## TL;DR

This paper investigates energy transfer dynamics between linear and nonlinear states in the one-dimensional quintic nonlinear Schrödinger equation, highlighting multi-resonance phenomena and long-period wave energy exchanges.

## Contribution

It extends previous work by simulating multi-resonance energy exchanges in long-period waves within the quintic nonlinear Schrödinger framework.

## Key findings

- Confirmed conservative wave energy exchange in multi-mode interactions
- Demonstrated multi-resonance energy transfer in long-period waves
- Validated theoretical predictions through numerical simulations

## Abstract

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.