Dark solitons in nonlocal media: variational analysis

The propagation of dark solitons is systematically investigated in a weakly nonlocal self-defocusing Kerr-type nonlinear medium. Based on the variational principle, we get an analytical solution of such nonlocal dark solitons. We also clearly give the expression describing the transverse velocity of the dark solitons. We find that the width of the dark solitons is related to the degree of nonlocality and the grayness of the solitons, that there exists a threshold of the degree of nonlocality for such nonlocal dark solitons, and that, as the degree of nonlocality increases, the solitons' velocity will decrease. We also demonstrate the stability of the nonlocal dark solitons.