  A minimal Lorentz surface in $\mathbb R^4_2$ is said to be of general type if
its corresponding null curves are non-degenerate. These surfaces admit
canonical isothermal and canonical isotropic coordinates. It is known that the
Gauss curvature $K$ and the normal curvature $\varkappa$ of such a surface
considered as functions of the canonical coordinates satisfy a system of two
natural PDEs. Using the Weierstrass type representations of the corresponding
null curves, we solve explicitly the system of natural PDEs, expressing any
solution by means of four real functions of one variable. We obtain the
transformation formulas for the functions in the Weierstrass representation of
a null curve under a proper motion in $\mathbb R^4_2$. Using this, we find the
relation between two quadruples of real functions generating one and the same
solution to the system of natural PDEs.
