  Structures in circumstellar matter reflect both fast processes and
quasi-equilibrium states. A geometrical diversity of emitting circumstellar
matter is observed around evolved massive stars, in particular around B[e]
supergiants. We recapitulate classical analytical tools of linear and
non-linear potential theory, such as Cole-Hopf transformations and
Grad-Shafranov theory, and develop them further to explain occurrence of the
circumstellar matter structures and their dynamics. We use potential theory to
formulate the non-linear hydrodynamical equations and test dilatations of the
quasi-equilibrium initial conditions. We find that a wide range of flow
patterns can basically be generated and the time scales can switch, based on
initial conditions, and lead to eruptive processes, reinforcing that the
non-linear fluid environment includes both quasi-stationary structures and fast
processes like finite-time singularities. Some constraints and imposed
symmetries can lead to Keplerian orbits, while other constraints can deliver
quasi-Keplerian ones. The threshold is given by a characteristic density at the
stellar surface.
