Novel (2+1) and (3+1) forms of the Biswas-Milovic equation and optical soliton solutions via two efficient techniques

Abstract

Purpose: The aim of this manuscript is to present the novel (2+1) and (3+1) forms of the Biswas-Milovic equation, which was introduced to the literature during 2010. The BiswasMilovic equation is one of the important equation to model the soliton propagation through optical waveguides and it has been the subject of many researches. In order to obtain basic optical soliton solutions (bright, dark, singular) of the introduced equations the efficient the new Kudryashov and the unified Riccati equation expansion methods have been utilized. Methodology: After, introducing the nonlinear partial differential equations (NLPDEs) of the (2+1) and (3+1)-dimensional Biswas-Milovic equations ((2+1)-BME and (3+1)-BME), firstly, the necessary complex wave transformations are defined. Then nonlinear ordinary differential (NODE) forms of the BMEs are obtained by applying the complex wave transformations. Later, the algorithms of the new Kudryashov (nKM) and the unified Riccati equation expansion method (UREEM) are given and applied to this NODEs form. The polynomial form, the linear algebraic system, and the appropriate solution sets are obtained, respectively. Finally, optical soliton solutions of the introduced BME equations are gained by combining the serial form, solution function, solution sets, wave transform and the applied method. Findings: It has been shown that the introduced (2+1)-BME and (3+1)-BME equations produce optical soliton solutions, and the basic optical solitons are obtained by the proposed methods and presented graphically. Moreover, it has been seen that the BME equation is an effective equation not only in (1+1)-dimension but also in modeling (2+1) and (3+1)-dimensional optical soliton behavior in fiber. Originality: The (2+1)-BME and (3+1)-BME equations presented in the study have been introduced for the first time in this article.