Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Abstract

This investigation focuses on the construction of novel dark and singular soliton solutions for the Hirota equation, which models the propagation of ultrashort light pulses in optical fibers. Initially, we employ a wave variable transformation to convert the physical model into ordinary differential equations. Utilizing extended rational sinh–cosh and sine–cosine techniques, we derive an abundant soliton solution for the transformed system. By plugging these explicit solutions back into the wave transformation, we obtain dark and singular soliton solutions for the Hirota equation. The dynamic evolution of dark soliton profiles is then demonstrated, with a focus on varying physically significant parameters such as wave frequency, strength of third-order dispersion, and wave number. Furthermore, a comprehensive analysis is examined to elucidate how the dark and singular soliton profiles undergo deformation in the background influenced by these arbitrary parameters. The findings presented in this study offer valuable insights that could potentially guide experimental manipulation of dark solitons in optical fibers.