Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation
Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation
复制标题
少周期光流氓波：复杂的修正 Korteweg-de Vries 方程
DOI：
10.1103/physreve.89.062917
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发表时间：
2014-06-18
影响因子：
2.4
通讯作者：
Erdelyi, R.
中科院分区：
文献类型：
--
作者：
He, Jingsong;Wang, Lihong;Erdelyi, R.
在这篇文章中，我们把复修正的Korteweg-de Vries(MKdV)方程看作一个少周期光脉冲模型。利用Lax对构造了广义Darboux变换，系统地产生了一阶、二阶和三阶无赖波解，并详细分析了高阶无赖波的演化本质。在详细的数值和分析研究的基础上，我们根据高阶流氓波的内在结构，即基本波、三角波和环波，对它们进行了分类。我们还根据标准和非标准分解提出了几种新的流氓波模式。本文的结果用有理解的形式解释了高阶流氓波的推广。应用轮廓线方法得到了复数mKdV方程和非线性薛定谔方程的一阶流氓波的长度和宽度的解析公式。在非线性光学中，高阶流氓波解对于产生高功率、短周期的光脉冲将是非常有用的，这将在超短脉冲技术领域得到应用。
In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical investigations, we classify the higher-order rogue waves with respect to their intrinsic structure, namely, fundamental pattern, triangular pattern, and ring pattern. We also present several new patterns of the rogue wave according to the standard and nonstandard decomposition. The results of this paper explain the generalization of higher-order rogue waves in terms of rational solutions. We apply the contour line method to obtain the analytical formulas of the length and width of the first-order rogue wave of the complex mKdV and the nonlinear Schrodinger equations. In nonlinear optics, the higher-order rogue wave solutions found here will be very useful to generate high-power few-cycle optical pulses which will be applicable in the area of ultrashort pulse technology.