Sensitivity characteristics of the Hirota–Maccari system in nonlinear materials

This study explores the nonlinear Hirota-Maccari ([Formula: see text]) system, a foundational model originally formulated by R. Hirota and A. Maccari to capture intricate nonlinear phenomena across diverse physical domains, notably electromagnetic wave propagation in nonlinear optical media. We provide closed-form and computational techniques for delineating the system's properties using the Khater II and Bernoulli sub-equation processes, as well as an auxiliary exponential cubic B-spline collocation scheme. The Hamiltonian function [Formula: see text] is used for bifurcation analysis, revealing equilibrium points, chaotic attractors, quasi-periodic orbits, and sensitivity to initial conditions in the associated planar dynamical system. This investigation deepens insight into the [Formula: see text] model by highlighting influential parameters and establishing theoretical bridges to other nonlinear evolution equations. The results have broad relevance to both theoretical analysis and applied sciences, enhancing conceptual understanding of nonlinear wave dynamics and offering potential utility in real-world technological contexts. By introducing refined mathematical structures and outlining prospective avenues for future study, this work contributes meaningfully to the advancement of nonlinear evolution theory.