Engineering Faculty, Işık University, İstanbul, Turkey.
Phys Rev E. 2016 Jun;93(6):062215. doi: 10.1103/PhysRevE.93.062215. Epub 2016 Jun 15.
In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field.
本文分析了 Kundu-Eckhaus 方程（KEE）的随机波浪谱。我们将研究结果与它们的非线性薛定谔方程（NLSE）类似物进行了比较，并表明单个随机波浪谱与其 NLSE 类似物有明显的差异。一个显著的区别是，在随机波浪在时间上变得明显之前，三角谱的单边发展。我们还表明，增加随机波浪的偏度会导致三角傅里叶谱的不对称性增加。此外，与 NLSE 类似物相比，KEE 的随机波浪的三角谱在其发展的早期阶段开始发展，尤其是对于较大的偏斜角。这一特征可用于增强随机波浪的预警时间。然而，我们表明，在具有许多谱分量的混沌波场中，三角谱仍然是主要属性，是通过调制不稳定性产生的典型波场的通用特征，而 KEE 的分析随机波浪谱的特征可能会在现实的混沌波场中被抑制。
