Dark and gray spatial optical solitons in Kerr-type nonlocal media

With the spectral renormalization method (the Fourier iteration method) we compute dark/gray soliton solutions in Kerr-type nonlocal media and find it agrees well with the analytical results. It is indicated when the characteristic nonlocal length is less than a certain critical value, the gray soliton's maximal transverse velocity does not vary with the characteristic nonlocal length, otherwise such maximal velocity decreases with the characteristic nonlocal length.