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This paper studies the perturbed Radhakrishnan–Kundu–Lakshmanan (RKL) equation and its special form, the generalized RKL equation. Kerr law nonlinearity is considered for both equations. The Riccati-Bernoulli sub-ODE technique is implemented to these nonlinear equations so that their optical solitons and complex wave solutions are retrieved. In order to derive a sequence of solutions of considered equations, Bäcklund transformation can be carried out. 3D and 2D graphics of some solutions are depicted for chosen suitable parameters.