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 $Δ^{(p)}\vec{x}=0$ and $Δ^{(p)}\vec{x}=-Λ(t,σ^r)\vec{x}$ give two sets of exact solutions.

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