Dynamics of matter–wave dark solitons in two-component Bose–Einstein condensates trapped in the parabolic external potential

Abstract

The cubic coupled Gross–Pitaevskii equation models the two-component Bose–Einstein condensates trapped in the parabolic external potential. A family of exact dark soliton solutions of the coupled Gross–Pitaevskii equation are constructed by similarity transformation and Hirota bilinear method. The dynamical behaviors of the matter–wave dark solitons are analyzed graphically. It is shown that the time-dependent nonlinearity can support exact matter–wave dark solitons in the two-component Bose–Einstein condensates. A special kind of matter–wave dark solitons are found, whose backgrounds decay to zero as t→∞.