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A minimal Lorentz surface in $\mathbb R^4_2$ is said to be of general type ifits corresponding null curves are non-degenerate. These surfaces admitcanonical isothermal and canonical isotropic coordinates. It is known that theGauss curvature $K$ and the normal curvature $\varkappa$ of such a surfaceconsidered as functions of the canonical coordinates satisfy a system of twonatural PDEs. Using the Weierstrass type representations of the correspondingnull curves, we solve explicitly the system of natural PDEs, expressing anysolution by means of four real functions of one variable. We obtain thetransformation formulas for the functions in the Weierstrass representation ofa null curve under a proper motion in $\mathbb R^4_2$. Using this, we find therelation between two quadruples of real functions generating one and the samesolution to the system of natural PDEs.

Explicit Solving of the System of Natural PDEs of Minimal Lorentz Surfaces in $\mathbb R^4_2$