  I conduct an analytical study of the interaction of jets, or a collimated
fast wind (CFW), with a previously blown asymptotic giant branch (AGB) slow
wind. Such jets (or CFWs) are supposedly formed when a compact companion, a
main sequence star or a white dwarf, accretes mass from the AGB star, forms an
accretion disk, and blows two jets. This type of flow, which is thought to
shape bipolar planetary nebulae (PNe), requires 3-dimensional gas dynamical
simulations, which are limited in the parameter space they can cover. By
imposing several simplifying assumptions, I derive simple expressions which
reproduce some basic properties of lobes in bipolar PNe, and which can be used
to guide future numerical simulations. I quantitatively apply the results to
two proto-PNe. I show that the jet interaction with the slow wind can form
lobes which are narrow close to, and far away from, the central binary system,
and which are wider somewhere in between. Jets that are recollimated and have
constant cross section can form cylindrical lobes with constant diameter, as
observed in several bipolar PNe. Close to their source, jets blown by main
sequence companions are radiative; only further out they become adiabatic,
i.e., they form high-temperature low-density bubbles that inflate the lobes.
This implies that radiative cooling must be incorporated in numerical codes
intended to study the formation of lobes in PNe.
