  We demonstrate that the 1D cylindrical version of the Grad-Shafranov equation
is more rich than classical self-similar ones, and more suitable for the
astrophysical jets we observe. In particular, it allows us to describe the
central (and, hence, the most energetic) part of the flow. Both relativistic
and non-relativistic versions are discussed. It is shown that taking into
account the finite pressure of the external media one can determine the
magnetic flux within the central core. We found as well that for
non-relativistic flows which are magnetically dominated near the origin the
solution can be constructed only in the presense of the oblique shock near the
base of a jet where the additional heating is to take place.
