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Optical soliton solutions of the Biswas-Arshed model by the $\tan(\circleddash/2)$ expansion approach

In this paper, we consider the Biswas-Arshed model (BAM) with nonlinear Kerr and power law. We integrate these nonlinear structures of the BAM to obtain optical exact solitons that passing through the optical fibers. To retrieve the solutions, we apply the $\tan(\circleddash/2)$ expansion integral scheme to the structures of the BAM nonlinearity. The novel solutions present optical shock wave, double periodic optical solitons, interaction between optical periodic wave and optical solitons, and optical periodic and rogue waves for both structures of the model. It is shown that the amplitude of the periodic double solitons waves gradually increases and reached the highest peak at the moment of interaction, and it goes to diminish for a much larger time. In fact, we show that the amplitude of the wave for the interaction between periodic and optical solitons, gradually increases with beat phenomena. To the purpose, all these types of optical solitons can be frequently used to amplify or reduce waves for a certain hight. Moreover, we describe the physical phenomena of the solitons in graphically.