A system of the fourth-order nonlinear differential equations for description of wave propagation in optical fiber Bragg gratings is considered. This system of equations also takes into account arbitrary refractive index. The model includes non-local nonlinearity too. The studied system of equations is transformed into a system of ordinary differential equations using traveling wave variables. Compatibility conditions for the obtained system are defined and analyzed. Exact solutions of the model in the form of solitary waves are found.
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