New families of soliton solutions for the (2 + 1)-dimensional nonlinear evolution equation arising in nonlinear optics

This article aims to achieve families of new traveling wave solutions to the (2 + 1)-dimensional nonlinear evolution equation using three powerful analytical techniques: the general form of Kudryashov’s method, the Bernoulli sub-ODE method, and the extended direct algebraic method. Moreover, we use several graphics to highlight our findings. The resulting traveling wave solutions are presented by hyperbolic, trigonometric, rational, and exponential functions. Bright, dark, periodic, and singular soliton solutions are introduced, and the obtained solutions are critical in explaining the wave dynamics in various models. The main findings and graphs indicate that the used approaches are the most appropriate for solving the given model, which generated several deferent solutions. Moreover, the dynamics of the model’s produced solutions may be controlled by adjusting the values of the model’s parameters.