Computational method for obtaining solitary wave solutions of the (2+1)-dimensional AKNS equation and their physical significance

This study employs precise, accurate, and efficient analytical and numerical techniques to obtain novel and accurate solitary wave solutions for the (2+1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) equation. The Khater II (Khat II) method and extended cubic-B-spline (ECBS) scheme are utilized as recent computational and accurate numerical techniques, respectively, for investigating the AKNS equation and constructing highly precise solitary wave solutions. The stability characteristics of the obtained solutions are also analyzed to ensure their applicability. These solutions are characterized by their peak amplitudes, wave speeds, and widths. Through comparisons with previous numerical techniques, our proposed approach demonstrates superior effectiveness and reliability. The research is significant due to the application of the (2+1)-dimensional AKNS equation in modeling various physical phenomena, such as nonlinear optics, water waves, and plasma physics. The precise and efficient determination of solitary wave solutions not only enhances the understanding of these phenomena but also provides a valuable framework for practical applications. The results have substantial implications for comprehending complex wave dynamics in physical systems and serve as a valuable tool for further research and analysis in the field of wave dynamics.