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In this paper, we study the novel exact solutions of the (2+ 1)-dimensional Biswas–Milovic equation for the description of pulse propagation in optical fiber. We successfully constructed some important solutions, such as dark, singular, combined dark-singular soliton, singular periodic wave and rational function solutions, have been analytically obtained using the extended tanh method. These solutions might play an important role in the engineering and physics fields. It is shown that the considered method provide a straightforward and powerful mathematical tool for solving problems in nonlinear optic and other physical phenomena.