<p>This paper investigates, for the first time, the soliton dynamics, exact solutions, and chaotic behavior of the Triki–Biswas equation under multiplicative white noise, using the trial equation method and the complete discrimination system for polynomials. Traveling wave transformation and dynamical system analysis enable the theoretical identification of soliton and periodic wave solutions. On this basis, 37 exact solutions are systematically derived and classified by applying the complete discrimination system for polynomials. The results show that the stochastic averaging process alters the dynamical properties of the solutions, reducing their periodicity, leading to randomized, homogenized behavior. Visualization results confirm that the delay effect induced by multiplicative white noise primarily governs the variation in waveform amplitude. Furthermore, by introducing specific perturbations, we show that the system can exhibit chaotic dynamics triggered by external disturbances. This study provides new insights and a theoretical basis for a deeper understanding of the complete dynamical landscape of nonlinear models in noisy environments.</p>