Novel optical soliton solutions for the generalized integrable (2+1)- dimensional nonlinear Schrödinger system with conformable derivative

For the generalized integrable (2+1)-dimensional nonlinear Schrödinger system, new and creative analytical solutions were derived using a novel extended direct algebraic method incorporating conformable derivatives, which could be expressed in terms of elementary functions and yielded a variety of analytical solutions, such as single, optical periodic, and wave solitons. The analytical solutions provided key insights into the effects of conformable derivatives and temporal parameters on the behavior of optical solitons, such as their stability, propagation, and interaction. To further elucidate the dynamics of these solitons, 2D, 3D, and contour plots were created to provide a visual representation of the soliton's form, amplitude, and phase. This helps to better understand the behavior of the soliton and its potential applications in nonlinear equations. Based on the study's demonstration of the extended direct algebraic method's strength and versatility in obtaining analytical solutions for complex non linear systems, it may be a useful tool for solving a variety of nonlinear problems in science and engineering.