A classical formalism for the weakly nonlin-
ear instability analysis of a gravitating rotating viscoelas-
tic gaseous cloud in the presence of gyratory dark matter is
presented on the cosmic Jeans flat scales of space and time.
The constituent neutral gaseous fluid (NGF) and dark matter
fluid (DMF) are inter-coupled frictionally via mutual gravity
alone. Application of standard nonlinear perturbation tech-
niques over the complex gyro-gravitating clouds results in a
unique conjugated pair of viscoelastic forced Burgers (VFB)
equations. The VFB pair is conjointly twinned by correla-
tional viscoelastic effects. There is no regular damping term
here, unlike, in the conventional Burgers equation for the
luminous (bright) matter solely. Instead, an interesting lin-
ear self-consistent derivative force-term naturalistically ap-
pears. A numerical illustrative platform is provided to reveal
the micro-physical insights behind the weakly non-linear
natural diffusive eigen-modes. It is fantastically seen that
the perturbed NGF evolves as extended compressive solitons
and compressive shock-like structures. In contrast, the per-
turbed DMF grows as rarefactive extended solitons and hy-
brid shocks. The latter is micro-physically composed of rar-
efactive solitons and compressive shocks. The consistency
and reliability of the results are validated in the panoptic
light of the existing reports based on the preeminent non-
linear advection-diffusion-based Burgers fabric. At the last,
we highlight the main implications and non-trivial futuristic
applications of the explored findings.

EB00000004052K

Available

• Instability analysis of cosmic viscoelastic gyro-gravitating clouds in the presence of dark matter