Optical solitons for the Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion

For the first time, the optical soliton solutions of the (1 + 1)-dimensional Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion are intended to be analyzed in detail. To attain this purpose, the new Kudryashov and the Kudryashov auxiliary equation technique are successfully implemented. Moreover, the impacts of model parameters on the soliton dynamics are scrutinized. The complex wave transformation is utilized to get the nonlinear ordinary differential equation form and to generate soliton solutions, the presented methods are performed. Finally, various graphical illustrations were derived and detailed comments were added on the solution results. The new Kudryashov approach and the Kudryashov auxiliary equation technique have been successfully performed and soliton solutions obtained. W-shape soliton was acquired with the new Kudryashov approach and the bright soliton was acquired with the Kudryashov auxiliary equation technique. Furthermore, diverse graphic descriptions that the resulting soliton solutions are obtained, and 2D graphs are presented and commented on. Since the Biswas-Milovic equation, which is the subject of much research, has an important role in nonlinear optics, different forms of the Biswas-Milovic equation are developed in the literature. The model in the presence of spatio-temporal dispersion was presented and scrutinized for the first time.