A theoretical evolutionary model to analyze the
dynamics of strongly nonlinear waves in inhomogeneous
complex astrophysical viscous clouds on the gravito-
electrostatic scales of space and time is procedurally set
up. It compositionally consists of warm lighter electrons
and ions (Boltzmanian); and cold massive bi-polar dust
grains (inertial fluids) alongside vigorous neutral dynam-
ics in quasi-neutral hydrodynamic equilibrium. Applica-
tion of the Sagdeev pseudo-potential method reduces the
inter-coupled structure equations into a pair of intermixed
forced Korteweg-de Vries-Burgers (f -KdVB) equations.
The force-terms are self-consistently sourced by inhomo-
geneous gravito-electrostatic interplay. A numerical illus-
trative shape-analysis based on judicious astronomical para-
metric platform shows the electrostatic waves evolving as
compressive dispersive shock-like eigen-modes. A unique
transition from quasi-monotonic to non-monotonic oscil-
latory compressive shock-like patterns is found to exist.
In contrast, the self-gravitational and effective perturba-
tions grow purely as non-monotonic compressive oscil-
latory shock-like structures with no such transitory fea-
tures. It is seen that the referral frame velocity acts as
amplitude-reducing agent (stabilizing source) for the elec-
trostatic fluctuations solely. A comparison in the prog-
nostic light of various earlier satellite-based observations
and in-situ measurements is presented. The paper ends
up with synoptic highlights on the main implications and
non-trivial applications in the interstellar space and cosmic
plasma environments leading to bounded structure forma-
tion.

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• Nonlinear waves in bipolar complex viscous astroclouds