A diverse array of optical solitons in the damped (2 + 1)-dimensional nonlinear Schrödinger equation via the modified exponential rational function method and other distinct strategies

This study addresses the damped (2 + 1)-dimensional nonlinear Schrödinger equation (DNLS) using innovative techniques, with a focus on elucidating the problem’s significance, employed methodologies, key findings, and unique contributions. We extensively explore the modified exponential rational function technique and other distinctive approaches, revealing a diverse range of wave solutions for DNLS equation. Notably, our research unveils new optical solutions, including bright and dark solitons, extracted under specific parameter conditions. The significance of this work is underscored by its contributions to nonlinear dynamics and optical physics. Our findings provide valuable insights into the intricacies of the DNLS equation, surpassing prior endeavors in the field by introducing novel methodologies and uncovering a wealth of solutions with broad applicability.