Randoux Stéphane, Gustave François, Suret Pierre, El Gennady
Université Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France.
Centre for Nonlinear Mathematics and Applications, Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.
Phys Rev Lett. 2017 Jun 9;118(23):233901. doi: 10.1103/PhysRevLett.118.233901.
We examine integrable turbulence (IT) in the framework of the defocusing cubic one-dimensional nonlinear Schrödinger equation. This is done theoretically and experimentally, by realizing an optical fiber experiment in which the defocusing Kerr nonlinearity strongly dominates linear dispersive effects. Using a dispersive-hydrodynamic approach, we show that the development of IT can be divided into two distinct stages, the initial, prebreaking stage being described by a system of interacting random Riemann waves. We explain the low-tailed statistics of the wave intensity in IT and show that the Riemann invariants of the asymptotic nonlinear geometric optics system represent the observable quantities that provide new insight into statistical features of the initial stage of the IT development by exhibiting stationary probability density functions.
我们在散焦三次一维非线性薛定谔方程的框架内研究可积湍流（IT）。这通过理论和实验两种方式完成，具体是通过实现一个光纤实验，其中散焦克尔非线性效应强烈主导线性色散效应。使用色散流体动力学方法，我们表明IT的发展可分为两个不同阶段，初始的预破裂阶段由相互作用的随机黎曼波系统描述。我们解释了IT中波强度的低尾统计特性，并表明渐近非线性几何光学系统的黎曼不变量代表了可观测量，通过展示平稳概率密度函数，为IT发展初始阶段的统计特征提供了新的见解。
