This paper studies the optical soliton solutions of the Biswas–Arshed equation with the help of two different techniques, such as the generalised exponential rational function (GERF) technique and Kudryashov’s simplest equation technique. TheGERFtechnique extracts distinct families of exact solitarywave solutions involving trigonometric function solutions, hyperbolic function solutions, rational function solutions, etc. After that, we apply Kudryashov’s simplest equation method in the context of Bernoulli and Riccati equations to attain different kindsof families of exact soliton solutions. All the acquired solutions of the equation have numerous applications in many branches of nonlinear sciences such as plasma physics, superconductivity, nonlinear optics, biophysics, starformation, quantum mechanics, etc. and many more connected fields of nonlinear wave sciences. The exact solitary wave solutions obtained by GERF technique and Kudryashov’s simplest equation technique are inmore generalisedform as they contained several arbitrary parameters. Subsequently, to understand the behaviour of deduced solutions, we graphically discuss the real part, imaginary part and modulus of these solutions by suitable choice of involved arbitrary parameters.