Kundu-Eckhaus方程的游荡波谱
Rogue Wave Spectra of the Kundu-Eckhaus Equation
摘要：
本文分析了Kundu-Eckhaus方程（KEE）的异常波谱。我们比较我们的研究结果与他们的非线性薛定谔方程（NLSE）的类似物，并表明，个别流氓波的光谱显着不同于他们的NLSE类似物。一个显著的区别是三角形频谱的单侧发展之前，流氓波变得明显的时间。此外，我们表明，增加的流氓波的偏度的结果在三角形傅立叶谱的不对称性增加。此外，三角形频谱的流氓波的KEE开始发展在其发展的早期阶段相比，他们的NLSE类似物，特别是对于较大的斜交角。该特征可用于增强异常波的早期预警时间。然而，我们表明，在一个混乱的波场与许多频谱成分的三角形频谱仍然是作为一个普遍的功能，通过调制不稳定性和KEE的分析流氓波频谱的特征可能会被抑制在一个现实的混沌波场的典型波场的主要属性。
英文摘要：
In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrodinger 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 the 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 wavefield with many spectral components the triangular spectra remains as the main attribute as a universal feature of the typical wavefields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wavefield.
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