Optical solitons of Biswas-Milovic model having spatio-temporal dispersion and parabolic law via a couple of Kudryashov?s schemes

Purpose: The aim of this scientific research is to examine the optical soliton solutions of the Biswas-Milovic equation, which has a prominent role in nonlinear optic studies, has been the subject of many researches, and still maintains its importance in this field, of the parabolic law form with the spatio-temporal dispersion. Methodology: First of all, the nonlinear differential equation form (NLODE) has been obtained in order to examine the optical solutions of the investigated problem. For this, the necessary wave transformations have been made and applied to the investigated problem. Two efficient methods, the Kudryashov and the new Kudryashov, have been utilized to obtain optical soliton solutions from the NLODE, by giving the algorithm of the methods. The soliton solutions have been achieved by obtaining the unknown parameters contained in both the problem and the methods. Graphical representations of the obtained optical soliton solutions and the necessary interpretations have been made in the relevant sections. Findings: Having the spatio-temporal dispersion, different optical soliton solutions of the Biswas-Milovic equation containing parabolic law have been successfully obtained by the applied the Kudryashov and the new Kudryashov methods. Originality: The form of the Biswas-Milovic equation examined within the scope of the article and the optical soliton solutions obtained in relation to this form have not been previously studied and the results have not been reported.