  We investigate the structure of dynamics of large self-gravitating
astrophysical systems using a self-interacting two-component model. We consider
two cases, galaxy clusters and cosmic walls, for illustrations. In both cases
stability analyses are conducted using perturbative expansion. We have found
that waves and solitons are easily generated in these systems. Our analysis
shows that dark matter can be Jeans unstable in the very inner regions of
galaxy clusters if it has a large internal degree of freedom. The dark matter
core may collapse under external perturbations. We also discuss dark-matter
oscillations in galaxy clusters and how mode growth and decay lead to heating
of intracluster medium. Our analysis shows that dark-matter solitons with both
positive and negative amplitudes can be excited in cosmic walls. Resonances in
soliton interaction could enhance gas condensation. The co-existence of the two
types of dark-matter solitons implies that bright filaments can arise in dark
voids.
