中文摘要：

By using the standard symmetry reduction method,the gray/dark solitons and periodic waves（gray/dark soliton lattice） are analytically studied for the nonlinear optical media with periodic nonlocal response.It is found that there are two critical points for the quantity β=ωm2/ω02,the multiplication of the square of the wave number（1/ω0）and the strength（wm2） of the nonlocality both for the soliton and periodic solutions.The soliton solution exists only for β≤ 1/4 and the soliton is a double well gray soliton for β > 1/8 while it is a single well gray soliton for β≤ 1/8.The soliton is dark only for β=1/4,otherwise it is a gray soliton.Similar critical points exist for the gray/dark soliton lattice solutions.

英文摘要：

By using the standard symmetry reduction method,the gray/dark solitons and periodic waves（gray/dark soliton lattice） are analytically studied for the nonlinear optical media with periodic nonlocal response.It is found that there are two critical points for the quantity β=ωm2/ω02,the multiplication of the square of the wave number（1/ω0）and the strength（wm2） of the nonlocality both for the soliton and periodic solutions.The soliton solution exists only for β≤ 1/4 and the soliton is a double well gray soliton for β > 1/8 while it is a single well gray soliton for β≤ 1/8.The soliton is dark only for β=1/4,otherwise it is a gray soliton.Similar critical points exist for the gray/dark soliton lattice solutions.