We study the dynamics and energy exchanges between a linear oscillator and a nonlinear interaction state for the one dimensional, quintic nonlinear Schrödinger equation. Grébert and Thomann [9] proved that there exist solutions with initial data built on four Fourier modes, that confirm the conservative exchange of wave energy. Captured multi resonance in multiple Fourier modes, we simulate a similar energy exchange in long-period waves.

中文翻译：

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五次非线性Schrödinger方程的能量传递模型和大周期边值问题

我们研究了一维，五次非线性Schrödinger方程的线性振荡器和非线性相互作用状态之间的动力学和能量交换。Grébert和Thomann [9证明存在以四种傅立叶模式为基础的初始数据的解决方案，证实了波能的保守交换。在多个傅立叶模式下捕获多共振，我们模拟了长周期波中的类似能量交换。