Annular structures in perturbed low mass disc-shaped gaseous nebulae I :
  general and standard models
  This is the first of two papers where we study analytical solutions of a
bidimensional low mass gaseous disc rotating around a central mass and
submitted to small radial perturbations. Hydrodynamics equations are solved for
the equilibrium and perturbed configurations. A wave-like equation for the gas
perturbed specific mass is deduced and solved analytically for several cases of
exponents of the power law distributions of the unperturbed specific mass and
sound speed. It is found that, first, the gas perturbed specific mass displays
exponentially spaced maxima, corresponding to zeros of the radial perturbed
velocity; second, the distance ratio of successive maxima of the perturbed
specific mass is a constant depending on disc characteristics and, following
the model, also on the perturbation's frequency; and, third, inward and outward
gas flows are induced from zones of minima toward zones of maxima of perturbed
specific mass, leading eventually to the possible formation of gaseous annular
structures in the disc. The results presented may be applied in various
astrophysical contexts to thin gaseous discs of negligible relative mass,
submitted to small radial perturbations.
