Abstract
We consider the nonlinear coupled mode equations with competing cubic-quintic-septic nonlinearities, describing propagation of femtosecond optical pulses through fiber Bragg grating structure. By means of the multiple scale analysis, the model is reduced into the perturbed nonlinear Schrödinger equation with non-Kerr terms and higher-order dispersions. The complex envelope function ansatz of Li is adopted to investigate general analytic solitary wave solutions and derive explicit bright and dark solitons for the resulting nonlinear Schrödinger type equation. The physical parameters of the shape preserving solutions such as power and pulse width are calculated in terms of the dependent model coefficients. The constraint conditions for the existence of exact solutions are presented.
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