<p>In this study, we investigated the exact analytical solutions of the combined Kairat-II-X equation by employing the generalized exponential rational function method, a unified model that integrates the dynamics of both the Kairat-II and Kairat-X equations. Using this analytical approach, we derived a comprehensive set of exact solutions that included various types of nonlinear wave structures, such as kink-type solitons, wave solitons, and singular soliton solutions. The solutions are validated through comprehensive visualizations presented in two-dimensional and three-dimensional graphical representations, demonstrating their physical relevance and mathematical consistency. The effect of the temporal parameter is systematically analyzed, revealing the significant impact of this parameter on wave propagation characteristics and solution behavior. The novelty of this work lies in deriving new exact solutions that reveal rich dynamical behaviors, while preserving structural stability during propagation. To validate the results, comprehensive visualizations are provided through three-dimensional, contour, and two-dimensional plots, demonstrating the physical relevance and mathematical consistency of the solutions. Overall, the findings advance the theoretical understanding of nonlinear wave phenomena and open new perspectives for applications in plasma physics, optical communications, and fluid dynamics.</p>