We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schr{o}dinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for longer propagation distance. Our analysis and numerical simulations are confirmed by experiments performed in optical fiber.

中文翻译：

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来自周期性相位调制连续波的色散传播的 Akhmediev 呼吸器特征

我们详细研究了在线性传播过程中使用正弦相位调制观察到的脉冲定位特征与在非线性 Schr{o}dinger 方程控制的系统中传播过程中 Akhmediev 呼吸器演变过程中观察到的脉冲定位特征之间的定性相似性。在最大聚焦点获得的轮廓确实呈现出非常接近的时间和光谱特征。如果这些轮廓的线性和非线性纵向演化在最大聚焦点附近相似，则它们可能会因传播距离较长而显着发散。我们的分析和数值模拟得到了在光纤中进行的实验的证实。