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This paper retrieves the vector-coupled version of the generalized anticubic nonlinearity model in fiber Bragg gratings. With the help of the trial equation approach and the complete discriminant system for polynomial, nine families of the optical solitons solutions and single traveling wave solutions for the fiber Bragg gratings with generalized anticubic nonlinearity are obtained. Under specific parameter values, three-dimensional diagrams, two-dimensional diagrams, density plots, and contour plots of the obtained solutions are displayed. Moreover, the solutions obtained in the paper further demonstrated their accurate physical behaviors.