  The expansion of a superbubble is investigated both analytically and
numerically. Our model implements the thin layer approximation in a vertical
profile of density as given by an isothermal self-gravitating disk. A precise
comparison with the results of numerical hydro-dynamics is given. Analogies are
drawn with the Kompaneets equation that includes the quadratic
hyperbolic-secant law in the list of the plane-parallel stratified media. An
astrophysical application is made to the superbubble connected with the two
worms 46.4+5.5 and 39.7+5.7. The effects of the rotation of the galaxy on the
simulated radius and on the velocity are introduced. The worms with their
strong limb-brightening visible on astronomical maps are explained in the
framework of image theory.
