Optical bullets with Biswas–Milovic equation having Kerr and parabolic laws of nonlinearity

The main motivation of the study is to present the (3+1) version of the Biswas–Milovic equation (BME) for the first time and to obtain effective bullet (soliton) solutions. In the literature, it is observed that this equation is generally solved in (1+1) form. The part of the (3+1) dimensional Biswas–Milovic equation containing Kerr law nonlinearity has been solved with new Kudryashov, and the part containing parabolic law nonlinearity solved with the classical Kudryashov method. In this study, we have presented two main models. The model involving Kerr law nonlinearity has been solved with new Kudryashov and one bright bullet obtained. The model containing parabolic law nonlinearity has been solved with classical Kudryashov and one kink bullet obtained. The originality of this study is that the both Kerr law and parabolic law forms of the (3+1) model has never been solved by the methods used in this article. In addition, as well as original bullet solutions, interesting bullet graphs have been obtained with appropriate parameter selections. Moreover the effects of the parameters have been analyzed in detail and explained clearly, with supportive 2d, 3d and contour graphic simulations.