Abstract
In this thesis,we analyze the existence,stability and mobility of gap solitons in photonic crystals with diffusion mechanism of the nonlinearity numerically.For the bands of Bragg gap,solitons with nonlocal effects are more stabilized and become more movable due to the combinations of non-locality effect and the oscillation tails of the wave packets. We show that gap solitons can revive an elastic-like collision even in the photonic systems due to non-locality.