Modulation instability and soliton families of the complex Ginzburg-Landau equation having the parabolic with nonlocal law of self-phase modulation

This paper acquaints the adopted parabolic with the nonlocal law of self-phase modulation form of the complex Ginzburg–Landau model, which regularizes the evolution of specific amplitudes of instability pulses in diverse dissipative systems. We employ the new Kudryashov and Sinh-Gordon equation expansion schemes to obtain bright and dark soliton families under particular conditions on the parameters of the physical model. Furthermore, the effect of diverse model parameters such as the chromatic dispersion, the parabolic law, and the nonlocal nonlinearity terms on the behaviors of bright and dark soliton solutions is also explored. We also search for modulation instability analysis for the model. The primary contribution of this study is the examination of a different version of the complex Ginzburg–Landau model, which is not yet available in the literature, along with the first comprehensive analysis of its modulation instability. Thus, this study highlights the practical and prompt results received by the Sinh-Gordon equation expansion scheme. Thus, this study is expected to offer meaningful implications for ongoing and future research within the framework of this model.