This study delves into the perturbed Radhakrishnan–Kundu–Lakshmanan ( \((p\mathcal {RKL})\) ) model, a pivotal component within nonlinear optics and communication engineering. In addressing this challenge, we employed the Bernoulli sub-equation function method and the Khater II method as analytical approaches, complemented by numerical solutions authenticated through the exponential cubic B–spline (ECBS) method. Our investigation yielded innovative solitary wave solutions, depicted elegantly through three-dimensional, two-dimensional, and contour plots. To ascertain the precision and dependability of these outcomes, we conducted a comparative analysis between analytical and numerical findings, visually presenting them via two-dimensional graphs. The implications of our discoveries are significant, offering insights into perturbations of optical solitons within nonlinear optical fibers. Our research effectively concludes that the proposed methodologies successfully solve the \(p\mathcal {RKL}\) model, yielding highly accurate solutions. Notably, our study introduces novelty to nonlinear optics by applying the Bernoulli sub-equation function (BSE) method, the Khater II (Kh II) method, and the exponential cubic B-spline (ECBS) method to the \(p\mathcal {RKL}\) model, with a specific focus on solitary wave solutions.
