Wide-spectrum optical soliton solutions to the time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law

The time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law and its soliton solutions have significant implications to examine the dynamics of optical solitons, self-phase modulation, optical beam propagation in nonlinear media, pulse propagation in optical fibers, nonlinear waveguides, and signal transmission systems. This study focuses on the investigation of different soliton solutions related to various aspects of optical solitons, including their formation, propagation traits, and stability analysis of the mentioned equation. Soliton solutions are able to carry out long-distance transmission without frequent amplification and regeneration. We exploit an advanced mathematical technique, the $(G^{\prime }/G,1/G)$-expansion method to descend and analyze the soliton solutions. As a result, a significant number of definitive and efficient solitons, such as compacton, bell-shaped, anti-peakon, breather, periodic, and singular solitons have resulted. The uniqueness of the obtained solutions is established by comparing them with previous results. Also, we discuss in detail the implications of fractional derivative and the application of the obtained solutions to optical fiber communication and other relevant fields. The findings of the present study provide valuable insights into the fundamental nature of optical solitons. These insights will contribute to the design and optimization of future optical networks, enabling the development of faster, more reliable, and higher-capacity communication systems.