Sun Zhi-Yuan, Yu Xin
Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.
International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China.
Phys Rev E. 2021 Jun;103(6-1):062203. doi: 10.1103/PhysRevE.103.062203.
Integrable nonlinear Schrödinger (NLS) systems provide a platform for exploring the propagation and interaction of nonlinear waves. Extreme events such as rogue waves (RWs) are currently of particular interest. However, the presence of disorder in these systems is sometimes unavoidable, for example, in the forms of turbulent current in the ocean and random fluctuation in optical media, and its influence remains less understood. Here, we report numerical experiments of two nearly-integrable NLS equations with the effect of disorder showing that the probability of RW occurrence can be significantly increased by adding weak system noise. Linear and nonlinear spectral analyses are proposed to qualitatively explain those findings. Our results are expected to shed light on the understanding of the interplay between disorder and nonlinearity, and may motivate new experimental works in hydrodynamics, nonlinear optics, and Bose-Einstein condensates.
可积非线性薛定谔（NLS）系统为探索非线性波的传播与相互作用提供了一个平台。诸如 rogue 波（RWs）之类的极端事件目前备受关注。然而，这些系统中无序的存在有时是不可避免的，例如以海洋中的湍流以及光学介质中的随机涨落等形式存在，而其影响仍未得到充分理解。在此，我们报告了两个具有无序效应的近可积 NLS 方程的数值实验，结果表明通过添加微弱的系统噪声可显著提高 RW 出现的概率。我们提出了线性和非线性频谱分析来定性解释这些发现。我们的结果有望为理解无序与非线性之间的相互作用提供启示，并可能推动流体动力学、非线性光学以及玻色 - 爱因斯坦凝聚体等领域的新实验工作。
