Nonlinear optical dynamics and complex wave structures in nonlinear dispersive media.

The research focuses on optical solitons and employs the generalized auxiliary equation technique to obtain soliton resolutions for the nonlinear Kairat-X equation. This equation considers wave number groups influenced by time and velocity dispersion in non-linear mediums. Because of their stability and numerous uses in signal processing, telecommunications, and quantum physics, optical solitons are appreciated. Novel periodic, exponential, and other soliton solutions are shown in the work, and the dynamics of the model are thoroughly examined using phase portraits, quasi-periodic patterns, Lyapunov exponents, 3D attractors, 2D power spectra, and sensitivity analysis. Various simulations show how noise intensity variations affect system sensitivity and instability through the assessment of stochastic sensitivity along with Poincaré, and Lyapunov analysis. These results provide a significant addition to the discipline.