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.
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