In this article, we analyze the dynamics of soliton transmission to the newly proposed Biswas–Arshed model which is considered in the absence of self-phase modulation. To compensate the negligibly small group velocity dispersion, this model includes spatio-temporal dispersion of higher order. We utilize the extended simplest equation method to find new exact solutions of the Biswas–Arshed equation with the aid of computer algebraic system Maple. Hyperbolic functions solutions, trigonometric functions solutions, rational functions solutions are obtained. Comparison of our new results obtained in this article for the considered model with the other well-known results are also provided.