Density waves in gravitational interacting particles

Apr 2019
My question is about system of infinite number of point like particles with gravitation interaction (classic newtonian interactions). I am interested in propagation of density waves in infinite system which can be considered to be in equilibrium, uniform density, 3D, with emphasis on much larger timescales than close encounters.

I read few chapters from Chandrasekhar's books and I tried to search for articles about it.
one article even stated that this issue was not yet solved in 3d:
(Statistical mechanics of 1D self-gravitating systems: the core–halo distribution)

I know this issue was investigated very carefully in context of spiral galaxies, but the timescales of close encounters in astronomical systems are very large in relation to the evolution time. When such limitation is imposed, it means that waves are propagated dispersively.
I remember that I encountered somewhere (but I don't remember exactly where) in a claim that if close encounter timescale is very short in regard to the evolution time, waves are propagated non-dispersively.

My questions are:
1. Do you know about an analysis of non-dispersive waves propagation in such a medium?
2. Can transverse waves exist in such a medium (in ideal gas it cannot)?

I really appreciate any help you can give me