Multiwaves and optical soliton solutions with the concatenation model in the optical fibers

In this study, we extract the different kinds of exact wave solutions to the concatenation model, which is a combination of the nonlinear Schrödinger equation, the Lakshmanan-Porsezian-Daniel model, and the Sasa-Satsuma model. We use the unified method to extract new solutions. This method yields a range of wave solutions with distinct shapes, such as optical soliton, optical elliptic, and optical rational soliton solutions. To ensure the results’ physical compatibility, we delineated the 2D and 3D plots using appropriate parametric values. The investigation of achieved soliton solutions will provide effective results across transcontinental distances and related phenomena. The method employed in this study is efficient, talented, and dependable for calculating soliton solutions in nonlinear models. We predict that the results obtained in this study will be significant for applications in optical fibers, plasma physics, the telecommunications industry, engineering, and many more. We construct the given equation plane dynamical system in the bifurcation analysis, and provide all possible phase portraits using the Galilean transformation. The last part of the study examines the modulation instability of the concatenation model.