Application of the unified method to solve the Biswas–Arshed model

We apply the unified method to retrieve optical soliton solutions of the Biswas–Arshed model (BAM) with the Kerr law nonlinearity in this paper. We first derive the ordinary differential form of this model from its partial differential form via a variable transformation. Then we add many new dynamical solitons of combo trigonometric, hyperbolic, and rational function solutions by Maple-18 package in this literature. The derived solutions exhibit some dynamics as singular solitons with exponentially increasing and decreasing amplitudes, singular solitons with gradually increasing and decreasing amplitudes, and singular solitons with constant amplitudes. Moreover, W-shaped solitons with multiple bright and dark waves, double periodic optical solitons with exponentially increasing and decreasing amplitudes, and double periods with symmetric and asymmetric amplitudes are obtained. Besides this, various dynamical properties of the obtained solutions are presented graphically. •The Biswas–Arshed model (BAM) with the Kerr law nonlinearity is considered.•The unified technique is applied to retrieve soliton solutions of the BAM model.•W-shaped solitons with multiple bright and dark waves are obtained.•3D and 2D plots are depicted by choosing suitable parametric values.