<p>In this paper, we focus on the exact solution of the extended (3+1)-dimensional Kairat-X equation proposed by Wazwaz, which mainly describes the trajectory of an optical pulse in an optical fiber and illustrates relations with the differential geometry of curves and equivalence aspects. Initially, by employing the three wave method, we successfully construct single-breathing wave solution, double-breathing wave solution, bright and dark soliton solutions. These solutions reveal the complex dynamic behavior of the interactions between soliton waves and periodic waves in the equation. Subsequently, we investigate the interaction of lump wave with three different functions using the positive quadratic function method. Moreover, we map the evolution process and energy distribution of lump waves in various environments. Finally, by applying the velocity resonance condition to the N-soliton solution, we obtain the soliton molecule solution, which reveals the interaction and collision characteristics between solitons.</p>