Exploring Multistability, Chaos, and Soliton Families in the Long–Short Wave Interaction Model

This research uses three analytical processes: the novel Kudryshov procedure, the direct algebraic approach, and the modified Kudryshov technique to acquire exact and analytical outcomes for the long–short wave interaction nonlinear problem. A variable transformation is applied to convert the system’s partial differential framework into an ordinary one. Thereafter, the governing model is analyzed using the methods mentioned above, which yield novel dynamic optical solitons. These solutions include bell-shaped solitons, multiple breathers with bright, dark, and dark–bright structures, as well as periodic breathers with bright, dark, and bright–dark forms. Demonstrated through stable solutions, these results validate the computational approach. Multistability and sensitivity are explored using employing planar dynamics. Various chaos-identifying tools such as bifurcation plots, return maps, Lyapunov exponents, and power spectrum plots are applied to test the chaotic analysis of the stated model. Moreover, quasi-periodic, periodic, and disordered patterns are derived from the presented equation. Additionally, graphical representations illustrate the dynamic aspects of the obtained solutions. Overall, the employed methodologies prove impactful, efficient, and relevant for tackling diverse nonlinear phenomena.