高阶非线性薛定谔方程的常返性：低dimensional analysis
Recurrence in the high-order nonlinear Schrödinger equation: a low dimensional analysis
摘要：
研究了深水波高阶非线性薛定谔方程（HONLS，也称为Dysthe方程）的三波截断。我们通过与数值模拟的比较来验证我们的方法，区分不同四阶项的影响，并根据拓扑结构对解决方案进行分类。这使我们能够正确地定义发生在Benjamin-Feir不稳定性的非线性阶段的临时谱上移，并为研究该模型的进一步推广提供了工具。
英文摘要：
We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deepwater waves (HONLS, also named Dysthe equation). We validate our approach by comparing it to numerical simulation, distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model.
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