  The threshold conditions for a rotating pancake-like asymmetric
quartic-quadratic confined condensate to break in two localized fragments, as
well as to produce giant vortex at the center within the vortex-pattern
distributions, are investigated within the Thomas-Fermi (TF) approximation and
exact numerical solution of the corresponding Gross-Pitaevskii (GP) formalism.
By comparing the TF predictions with exact GP solutions, in our investigation
with two different quartic-quadratic trap geometries, of particular relevance
is to observe that the TF approach is not only very useful to display the
averaged density distribution, but also quite realistic in establishing the
critical rotational conditions for the breakup occurrence and possible
giant-vortex formation. It provides almost exact results to define the contour
of the condensate distribution, even for high rotating system, after the system
split in two (still confined) clouds. The applicability of the Feynman rule to
the vortex distribution (full-numerical GP solutions) is also being confirmed
for these non-homogeneous asymmetric trap configurations. This study is
expected to be relevant for manipulating the rotation and trap parameters in
addition to Feshbach resonance techniques. It can also be helpful to define
initial conditions for any further studies on dynamical evolution of vortex
pattern distributions.
