A simple ansatz for obtaining exact solutions of high dispersive nonlinear Schro¨dinger equations in fiber Bragg gratings

We present solitary wave solutions for the perturbed nonlinear Schro¨dinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schro¨dinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe bright and dark Bragg solitons properties in the same expressions and their amplitude may approach nonzero when the time variable approaches infinity. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in fiber Bragg grating.