  We study the dynamics of Bose-Einstein condensate coupled to a waveguide with
parity-time symmetric potential in the presence of quadratic-cubic nonlinearity
modelled by Gross-Pitaevskii equation with external source. We employ the
self-similar technique to obtain matter wave solutions, such as bright,
kinktype, rational dark and Lorentzian-type self-similar waves for this model.
The dynamical behavior of self-similar matter waves can be controlled through
variation of trapping potential, external source and nature of nonlinearities
present in the system.
