  The classical approach to visualizing a flow, in terms of its streamlines,
motivates a topological/soft-analytic argument for constrained variational
equations. In its full generality, that argument provides an explicit formula
for completely integrable solutions to a broad class of n-dimensional
quasilinear exterior systems. In particular, it yields explicit solutions for
extremal surfaces in Minkowski space and for Born--Infeld models.
