The Peregrine soliton is often considered as a prototype of rogue waves. After recent advances in the semiclassical limit of the one-dimensional focusing nonlinear Schrödinger equation [M. Bertola and A. Tovbis, Commun. Pure Appl. Math. 66, 678 (2013)0010-364010.1002/cpa.21445] this conjecture can be seen from another perspective. In the present paper, connecting deterministic and statistical approaches, we numerically demonstrate the effect of the universal local emergence of Peregrine solitons on the evolution of statistical properties of random waves. Evidence of this effect is found in recent experimental studies in the contexts of fiber optics and hydrodynamics. The present approach can serve as a powerful tool for the description of the transient dynamics of random waves and provide new insights into the problem of the rogue waves formation.

中文翻译：

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一维聚焦非线性薛定ding方程中局部百富勤孤子出现对随机波统计的影响。

百富勤孤子通常被认为是流浪的原型。经过最近的发展，一维聚焦非线性薛定ding方程的半经典极限[M．Bertola和A.Tovbis，社区。纯应用 数学。66，678（2013）0010-364010.1002 / cpa.21445]这个猜想可以从另一个角度看到。在本文中，结合确定性和统计方法，我们用数值方法证明了百富勤孤子的普遍局部出现对随机波统计特性演变的影响。在近期的光纤和流体动力学实验研究中发现了这种效应的证据。本方法可以用作描述随机波瞬态动力学的有力工具，并提供对流浪波形成问题的新见解。