<p>This paper examines optical soliton solutions of the Biswas–Milovic equation with cubic–quintic–septic–nonic nonlinearities, which generalize the nonlinear Schrödinger model to describe high-intensity wave propagation. Using the new mapping technique, several soliton solutions are obtained in terms of hyperbolic and trigonometric functions. The accuracy of these solutions is confirmed using symbolic computation in Mathematica, while their physical behaviors are depicted through 2-dimensional, and 3-dimensional plots generated in Python. A comprehensive dynamical analysis comprising bifurcation structures, quasi-periodicity, multistability, and initial-condition sensitivity is conducted through phase portraits and time-series simulations. The findings clarify nonlinear wave processes with possible technological applications in fiber optics systems, plasmas, and Bose–Einstein condensates.</p>