Discovering optical soliton solutions in the Biswas-Milovic equation through five innovative approaches

Purpose: In recent years, depending on the development of models containing highly dispersive nonlinear equations, especially in the field of nonlinear optics, it has been important to obtain the solutions of these equations with analytical methods. This study presents some effective, reliable, and easily applicable solution techniques based on the well-known extended auxiliary equation. Besides, these techniques were applied to the Biswas-Milovic equation.Methodology: First, in order to achieve the ordinary differential equation structure of the Biswas-Milovic equation, the complex wave transform was given and utilized. Then, the algorithms, constraints of each proposed approach, and key points for their implementation were presented. In addition, the relations and transitivities between the methods are also interpreted. Second, analytical optical soliton solutions were obtained by applying the proposed techniques. Lastly, graphical simulations of optical soliton types represented by some solution functions are made.Findings: It has been shown that all of the proposed methods yield effective results in solving the Biswas-Milovic equation and can be used not only for nonlinear evolution equations but also for highly dispersive nonlinear optical equations. It has been observed that the methods have the capacity to be employed easily and do not require tedious calculus and algebraic manipulations.Originality: The work in the article has not been presented before.