Motion of a Bose--Einstein Condensate Bright Soliton Incident on a Step-Like Potential

The motion characteristics of a Bose--Einstein condensate bright soliton incident on a local step-like potential barrier are investigated analytically by means of the variational approach. The dynamics of the soliton-potential interaction is studied as well. Then the results are verified by direct numerical simulations of the Gross--Pitaevskii equation. It is found that a moving bright soliton can be reflected from or pass over a step-like potential in a controllable fashion, the critical velocity depends on the width of the soliton and the parameters of the step, and the motion trajectory of the soliton does not depend on its phase. The atom density envelope of the soliton is changed as the result of the interaction between the soliton and the step-like potential.