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A minimal space-like surface in Minkowski space-time is said to be of generaltype if it is free of degenerate points. The fact that minimal space-likesurfaces of general type in Minkowski space-time admit canonical parameters ofthe first (second) type implies that any minimal space-like surface isdetermined uniquely up to a motion in space-time by the Gauss curvature and thenormal curvature, satisfying a system of two PDE's (the system of naturalPDE's). In fact this solves the problem of Lund-Regge for minimal space-likesurfaces. Using canonical Weierstrass representations of minimal space-likesurfaces of general type in Minkowski space-time we solve explicitly the systemof natural PDE's, expressing any solution by means of two holomorphic functionsin the Gauss plane. We find the relation between two pairs of holomorphicfunctions (i.e. the class of pairs of holomorphic functions) generating one andthe same solution to the system of natural PDE's, i.e. generating one and thesame minimal space-like surface in Minkowski space-time.

Explicit Solving of the System of Natural PDE's of Minimal Space-like Surfaces in Minkowski Space-time