Laplace-Beltrami operator and exact solutions for branes

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 Δ(p)x→=0 and Δ(p)x→=−Λ(t,σr)x→ give two sets of exact solutions.