Asymmetric propagation of solitons in nonlinear media with gradual nonlocality

We investigate the propagation of solitons in homogeneous nonlocal nonlinear media and in media with gradual nonlinear nonlocality. We calculate the width and the maximum amplitude of solitons during propagation and demonstrate that solitons will propagate asymmetrically in the medium with gradual nonlinear nonlocality. Moreover, the propagation of solitons in the nonlinear medium with gradual nonlocality is independent of the forms of monotonically gradual nonlocalities. Finally, we investigate the ratio of width magnification quantitatively and demonstrate that the soliton with a particular input power maintains its width in one direction and suffers strong expansion in another direction. (paper)