  Proposed is a new approach to finding exact solutions of nonlinear $p$-brane
equations in $D$-dimensional Minkowski space based on the use of various
initial value constraints. It is shown that the constraints
$\Delta^{(p)}\vec{x}=0$ and $\Delta^{(p)}\vec{x}=-\Lambda(t,\sigma^r)\vec{x}$
give two sets of exact solutions.
