  Abstract This is the first of two papers where we study analytical solutions
of a bidimensional low mass gaseous disc slowly rotating around a central mass
and submitted to small radial periodic 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 slowly rotating
thin gaseous discs of negligible relative mass, submitted to small radial
periodic perturbations.
