一个扩展的Kundu-Eckhaus方程用于模拟混沌波流场中的异常波动力学
An extended Kundu-Eckhaus equation for modeling dynamics of rogue waves in a chaotic wave-current field
摘要：
在本文中，我们提出了一个扩展的Kundu-Eckhaus方程（KEE）的动力学建模的斜流氓波出现在附近的波阻塞点，由于反向电流。我们提出的方程是一个KEE与一个额外的潜在的条款，因此，在本文中提出的结果可以很容易地推广到研究的流氓波和超短（飞秒）脉冲的KEE的量子隧穿性质。在扩展的KEE框架下，数值模拟表明海流的混沌扰动触发了海面上的流氓波。我们提出并实现了一个分裂的步骤计划，并表明，我们提出的扩展KEE是不稳定的随机混沌扰动在当前的配置文件。这些扰动将单色波场转变为具有许多峰的混沌海状态。我们的数值计算表明，由于扰动的流氓波的形状在当前的配置文件密切遵循的形式合理流氓波的解决方案，特别是对中心峰。我们还讨论了混沌电流扰动的大小对流氓波发生统计的影响。
英文摘要：
In this paper we propose an extended Kundu-Eckhaus equation (KEE) for modeling the dynamics of skewed rogue waves emerging in the vicinity of a wave blocking point due to opposing current. The equation we propose is a KEE with an additional potential term therefore the results presented in this paper can easily be generalized to study the quantum tunneling properties of the rogue waves and ultrashort (femtosecond) pulses of the KEE. In the frame of the extended KEE, we numerically show that the chaotic perturbations of the ocean current trigger the occurrence of the rogue waves on the ocean surface. We propose and implement a split-step scheme and show that the extended KEE that we propose is unstable against random chaotic perturbations in the current profile. These perturbations transform the monochromatic wave field into a chaotic sea state with many peaks. We numerically show that the shapes of rogue waves due to perturbations in the current profile closely follow the form of rational rogue wave solutions, especially for the central peak. We also discuss the effects of magnitude of the chaotic current perturbations on the statistics of the rogue wave occurrence.
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