  We study the dynamics of a dark-bright soliton interacting with a fixed
impurity using a mean-field approach. The system is described by a vector
nonlinear Schrodinger equation (NLSE) appropriate to multicomponent
Bose-Einstein condensates. We use the variational approximation, based on
hyperbolic functions, where we have the center of mass of the two components to
describe the propagation of the dark and bright components independently.
Therefore, it allows the dark-bright soliton to oscillate. The fixed local
impurity is modeled by a delta function. Also, we use perturbation methods to
derive the equations of motion for the center of mass of the two components.
The interaction of the dark-bright soliton with a delta function potential
excites different modes in the system. The analytical model capture two of
these modes: the relative oscillation between the two components and the
oscillation in the widths. The numerical simulations show additional internal
modes play an important role in the interaction problem. The excitation of
internal modes corresponds to inelastic scattering. In addition, we calculate
the maximum velocity for a dark-bright soliton and find it is limited to a
value below the sound speed, depending on the relative number of atoms present
in the bright soliton component and excavated by the dark soliton component,
respectively. Above a critical value of the maximum velocity, the two
components are no longer described by one center of mass variable and develop
internal oscillations, eventually breaking apart when pushed to higher
velocities. This effect limits the incident kinetic energy in scattering
studies and presents a smoking gun experimental signal.
