  We study time-like surfaces in the three-dimensional Minkowski space with
diagonalizable second fundamental form. On any time-like W-surface we introduce
locally natural principal parameters and prove that such a surface is
determined uniquely (up to motion) by a special invariant function, which
satisfies a natural non-linear partial differential equation. This result can
be interpreted as a solution of the Lund-Regge reduction problem for time-like
W-surfaces with real principal curvatures in Minkowski space. We apply this
theory to linear fractional time-like W-surfaces and obtain the natural partial
differential equations describing them.
