This study investigates the dynamics of ultrashort light pulses in an inhomogeneous optical medium exhibiting all orders of nonlinearity up to the ninth order. The research focuses on exploring the existence and properties of self-similar solitons while varying cubic, quintic, septic, and nonic nonlinearities, group velocity dispersion, and loss or gain. It is found that the transmission system supports the existence of novel types of self-similar bright and dark pulses in the presence of various physical processes. Importantly, these self-similar localized waves exhibit a linear chirp, a crucial factor for achieving effective pulse amplification or compression. Based on the chirp property, the dynamical behaviors of these self-similar waveforms are discussed in a periodically distributed amplification system. The findings highlight that the shape and dynamics of these chirped self-similar pulses can be precisely controlled by selecting appropriate profiles for gain or loss, nonlinearity, and dispersion. Additionally, the research numerically discusses the interaction dynamics between two and three adjacent solitons.

中文翻译：

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具有三次-五次-septic-nononic形式自相位调制的啁啾自相似光学孤子

这项研究研究了非均匀光学介质中超短光脉冲的动力学，该介质表现出所有阶的非线性，直至九阶。该研究的重点是探索自相似孤子的存在和性质，同时改变三次、五次、脓毒和非线性非线性、群速度色散以及损耗或增益。研究发现，在存在各种物理过程的情况下，传输系统支持新型自相似明脉冲和暗脉冲的存在。重要的是，这些自相似的局域波表现出线性调频，这是实现有效脉冲放大或压缩的关键因素。基于线性调频特性，讨论了周期性分布放大系统中这些自相似波形的动态行为。研究结果强调，通过选择适当的增益或损耗、非线性和色散分布，可以精确控制这些啁啾自相似脉冲的形状和动态。此外，该研究还以数值方式讨论了两个和三个相邻孤子之间的相互作用动力学。