Rogue waves in integrable turbulence: semi-classical theory and fast measurements
Rogue waves in integrable turbulence: semi-classical theory and fast measurements
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DOI：
10.1088/978-0-7503-1460-2ch12
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
P. Suret;G. El;M. Onorato;S. Randoux
中科院分区：
文献类型：
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作者：
P. Suret;G. El;M. Onorato;S. Randoux
当有噪声的初始数据被发射到由可积波动方程描述的系统中时，可积湍流产生。近年来，对可积湍流的复杂动力学和非高斯统计的研究已成为一个日益发展的基础性研究领域。在这一章中，我们将展示如何最近的理论结果中获得的半经典（零色散）限制的聚焦一维非线性薛定谔方程（NLSE）可以与可积湍流的现象。的半经典NLSE分析的结果之一是在有限间隙理论的框架，也被称为周期性逆散射变换（IST）的演化的渐近描述，我们展示了如何周期性IST可以用来表征可积湍流。最后，我们回顾光纤实验致力于研究（近）可积湍流。特别是，我们如何快速测量技术（时间透镜，时间显微镜，光学采样）现在允许详细研究的复杂和快速的动力学所产生的部分相干波在光纤中的传播。这些实验为半经典理论的一些基本预言提供了物理证实。
Integrable turbulence arises while noisy initial data are launched into a system described by an integrable wave equation. Over recent years, the study of the complex dynamics and non-Gaussian statistics in integrable turbulence has become a growing and fundamental field of research. In this chapter, we show how recent theoretical results obtained in the semi-classical (zero-dispersion) limit of the focusing one dimensional nonlinear Schrodinger equation (NLSE) can be related to the phenomenon of integrable turbulence. One of the outcomes of the semi-classical NLSE analysis is an asymptotic description of the evolution in the framework of finite-gap theory, also known as periodic inverse scattering transform (IST), and we show how this periodic IST can be used to characterize integrable turbulence. Finally, we review optical fiber experiments devoted to the study of (near) integrable turbulence. In particular, we show how fast measurement techniques (time lens, time microscope, optical sampling) now allow the detailed study of the complex and fast dynamics arising from the propagation of partially coherent waves in optical fibers. These experiments provide physical confirmation of some fundamental predictions of the semi-classical theory.