Bifurcations and stability of gap solitons in periodic potentials

We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrödinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays, optically-induced photonic lattices, and Bose-Einstein condensates loaded onto an optical lattice. We study bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum, and show that gap solitons can …