Evolvement between bright and dark soliton of condensates

By using Darboux transformation method, we study analytically the nonlinear dynamics properties of Bose-Einstein condensates trapped in an stable external poten tial. It is shown that the strength of inter-atomic interaction condensate has an important effect on its nonlinear dynamics properties. When atom-atom repulsive interaction of condensate is strong enough, there only exhibits bright soliton. While the inter-atomic repulsive interaction is less than a critical value, the alternative evolvement phenomenon between bright and dark soliton appears.