This paper retrieves the optical solitons to Biswas-Arshed equation (BAE) which is deliberated in the lack of self-phase modulation by applying the new extended hyperbolic function method (EHFM). Novel constructed solutions have the shape of bright, singular, periodic singular, and dark solitons. The achieved solutions contain key applications in engineering and physics. These solutions define the wave performance of the governing models, actually. The outcomes disclose that our scheme is very active and reliable. The acquired results are illustrated by 3-D and 2-D graphs to understand the real phenomena for such sort of non-linear models.