Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion.

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

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.