Unidirectional flow of solitons with nonlinearity management

Unidirectional flow of solitons is obtained with a localized modulation of the nonlinearity strength. The modulation takes the shape of an asymmetric double well with a slight difference between the potential depths. The results were established using numerical computations and then verified qualitatively using a variational approach. Our results suggest that the most important physics at the origin of the unidirectional flow is the excitation of the breathing modes in the scattering region. Simplified variational equations of motion suggested that the phenomenon can be observed if the soliton is scattered by a generic asymmetric effective double potential well.