M-shape, lump, homoclinic breather and other soliton interaction of the Landau-Ginzburg-Higgs model in nonlinear fiber optics

This study investigates the intricate dynamics of different types of solitons and their interactions within the framework of the Landau-Ginzburg-Higgs model as applied to nonlinear fiber optics. Employing the Hirota bilinear transformation technique, we derive a range of analytical soliton solutions, and demonstrating their rich and diverse behaviors. The proposed methodology provides a more comprehensive framework for analyzing transport processes by expanding these equations. M-shaped rational wave solutions with one kink, M-shaped rational waves with two kinks having bright and dark effects, periodic cross-kink with bright and dark waves, lump mixed-type waves, homoclinic breathers, and breather waves are among the various types of solitons. These many waveforms make it clear, soliton movement within optical fiber is extremely essential. They also offer valuable information that could influence soliton-based signal processing, optical communication systems, drug research, and other scientific fields. This extension of methodology aids in understanding the intricacy of soliton transport and identifying the intricate mechanisms. Additionally, by selecting various constant values, we create 3D and related contour plots to be aware of the physical interpretations of these solutions. Therefore, we get superior physical behaviors from these solutions.