Chirped self-similar optical solitons with cubic–quintic–septic–nonic form of self-phase modulation

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.