Bifurcations and Stability of Gap Solitons in Periodic Potentials

The existence, internal modes and stability of gap solitons in nonlinear periodic systems are discussed. The bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum are also discussed. It is found that gap solitons can appear near all upper or lower band edges of the spectrum, for defocusing or focusing nonlinearity, respectively. The results show that two types of gap solitons can bifurcate from each band edge and one out of those two is always unstable