Combined solitons in generalized coupled mode equations of a nonlinear optical Bragg grating

We discuss the existence of combined dark and antidark soliton forms or combined solitons in the generalized coupled mode equations of a nonlinear optical Bragg grating. These solitons are not allowed in the conventional coupled mode equations with uniform nonlinearity and exist outside the linear grating band gap. Their related Hamiltonian phase portrait was briefly reported by de Sterke [Phys. Rev. E 54, 1969 (1996)]. The explicit expressions for the corresponding solitons are presented, as well as their bifurcation process. We demonstrate the unstable propagation of perturbed combined solitons with zero velocity by means of direct numerical integration.