In our investigation, we’ve utilized an advanced computational technique, the modified exp \(-\phi (\zeta )\) -expansion method, to derive precise solitary wave solutions within the (2+1)–dimensional Ablowitz–Kaup–Newell–Segur ( \(\mathbb {AKNS}\) ) equation. These solutions, categorized by peak amplitudes, wave speeds, and widths, underscore the efficacy and reliability of our approach compared to conventional numerical methods. The significance of our study extends to practical applications of the (2+1)–dimensional \(\mathbb {AKNS}\) equation in modeling various physical phenomena, from nonlinear optics to water waves and plasma physics. Our research, by precisely determining solitary wave solutions, not only deepens our comprehension of these phenomena but also establishes a robust basis for practical applications.
