Enhanced sensitivity, stability, and dynamic behavior of the Biswas-Milovic equation with Kerr-Law non-linearity

This work derives novel exact solutions of the Biswas–Milovic nonlinear Schrödinger equation by employing the innovative Extended Modified Auxiliary Equation Mapping Technique, augmented with enhanced sensitivity analysis. The resulting bright, kink, anti-kink, and periodic soliton solutions provide deep insights into the complex dynamics of nonlinear wave propagation. To unravel the intricate behaviors of these solitons, we analyze phase trajectories, density distributions, and streamlines, with a particular focus on their sensitivity to initial conditions. Stability is rigorously evaluated through a Hamiltonian formalism, ensuring both analytical rigor and structural robustness. Collectively, these findings enrich the theoretical understanding of soliton dynamics and open new pathways for practical applications in advanced physical systems.