  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.
