  In this paper, the viscous cosmological dynamics are studied in the presence
of dark matter Bose-Einstein Condensation (BEC) by curved-FRW background. For
this purpose, we use the BEC regime rather than the normal dark matter (the
cold dark matter or the barotropic dark matter) with the dark matter Equation
of State (EoS) as $p_{dm} \propto \rho_{dm}^2$, which arises from the
gravitational form. Therefore, we obtain the corresponding continuity equations
with the existence of the universe components by considering an interacting
model with modified Chaplygin gas. Afterward, we derive the energy density and
the pressure of dark energy in terms of the redshift parameter. And then, by
introducing a parametrization function and fitting it with 51 supernova data
with the likelihood analysis, we find the cosmological parameters versus
redshift parameter. In what follows, we plot the corresponding dynamic graphs
proportional to redshift, and then we represent the universe is currently
undergoing an accelerated expansion phase. Finally, we explore the stability
and the instability of the present model with the sound speed parameter.
