Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects.
Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects.
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DOI：
10.1103/physreve.93.062217
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
Lei Wang;Jianhua Zhang;Chong Liu;Min Li;Feng-Hua Qi
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文献类型：
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作者：
Lei Wang;Jianhua Zhang;Chong Liu;Min Li;Feng-Hua Qi
研究了一类具有高阶效应的变系数非线性薛定谔方程。我们证明了在恒定背景下，呼吸子解可以转化为四种非线性波，包括多峰孤子、反暗孤子、周期波和W形孤子。特别地，解析地得到了群速度色散（GVD）和三阶色散（TOD）线性缩放的过渡条件。我们展示了几种弹性相互作用之间的转换的非线性波。讨论了多峰孤子的色散管理，指出GVD系数控制了孤子的峰数，而TOD系数具有压缩效应。增益和损耗对多峰孤子的振幅有影响。利用周期GVD调制光纤系统中Akhmediev呼吸子和Peregrine流氓波的多个压缩点，我们进一步导出了呼吸子多重出生和Peregrine梳。特别是，我们证明了通过适当选择周期性GVD调制的幅度，游隼梳可以转换为游隼壁。游隼壁可以被看作是一个介于无赖波和W形孤子之间的中间态。最后，我们发现零增长率的调制稳定区域与使用流氓波本征值的过渡条件相吻合。我们的研究结果可能是有用的实验控制和操纵的广义游隼无赖波的形成在不同的物理系统所模拟的vc-NLS方程的高阶效应。
We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W-shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W-shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.