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The modified extended tanh expansion method is applied to the perturbed Chen–Lee–Liu equation where the perturbation terms are with full nonlinearity. This method contributes a variety of optical soliton solutions including dark, singular, dark-singular soliton, singular periodic waves and rational function solutions to the perturbed Chen–Lee–Liu equation. The constraint conditions that validate the existence of the reported soliton solutions are acquired. The 2D, 3D, and the contour graphs of some of the obtained solutions are plotted.