Unveiling optical solitons and other solutions for fourth-order (2+1)-dimensional nonlinear Schrödinger equation by modified extended direct algebraic method

The (2+1)-dimensional nonlinear Schrödinger equation with fourth-order nonlinearity and dispersion is investigated in this study. Several optical solitons and other travelling wave solutions for the present problem are discovered using the modified extended direct algebraic method (MEDAM). Dark, bright, and singular soliton solutions are discovered, as well as hyperbolic, periodic, and singular periodic solutions, Jacobi elliptic function (JEF) solutions, Weierstrass elliptic doubly periodic solutions, exponential, and rational solutions. The solutions obtained can be utilized to gain a better understanding of the properties of some models in the field of optics, mechanics of fluids, and plasmas’ physics. The results are innovative and demonstrate the simplicity, accuracy, and applicability of the proposed method for a wide range of different mathematical and physical applications. To help readers physically grasp the acquired solutions, graphical representations of various types of the extracted solutions are provided.