Some New Mixed and Complex Soliton Behaviors and Advanced Analysis of Long-Short-Wave Interaction Model

The main objective of this research is to investigate various important soliton solutions for long-short-wave interaction model (LSWI) through the application of the new extended direct algebraic methodology. Thorough investigation and accurate verification, of hyperbolic, single and periodic, mixed-wave solutions as well as mixed periodic, shock soliton, different complex combination solutions, mixed trigonometric solutions, trigonometric solutions, shock results, singular solution, mixed singular results, mixed complex solitary wave outcomes, along with mixed shock singular solution as well as the mixed trigonometric solution are discovered. Advanced solitary wave solitons are generated by modifying the values of the parameters implicated in the derived solutions. The importance of these solitons in the model is illustrated via contour plots, density plots, 2D and 3D visualizations. Additionally, the dynamical investigation is established, and then sensitivity analysis, as well as bifurcation analysis, are illustrations to depict various aspects. The obtained bifurcation findings show the dynamic behavior of long-short-wave interaction model from a geometric perspective. Transmission of optical solitons via nonlinear optics is provided by the obtained results. The wave dynamics of the solutions are shown to provide a more physical viewpoint on the outcomes, helping the reader to better understanding the nonlinear wave equation that represents physical processes.