Bifurcations and optical solitons for the coupled nonlinear Schrodinger equation in optical fiber Bragg gratings

The main attention of this work focuses on studying the bifurcations and dispersive optical solitons for the coupled nonlinear Schrodinger equation in optical fiber Bragg gratings. First of all, with the help of bifurcation method of planar dynamical systems, the system's Hamiltonian and the orbits phase portraits have been found. As you can see, we construct the dark and singular solitons to this system. In addition to, some other optical solitons are derived by using the polynomial complete discriminant method and computer algebra with symbolic computation. In particular, it is worth to noting that some of the solutions which have been obtained in this work are new and not available in the known references. As a consequence, the obtained optical soliton solutions substantially improve or complement the corresponding conditions in the known references. Finally, in order to understand mechanisms of complex physical phenomena and dynamical processes for this system, we draw the two-dimensional and three-dimensional graphs.