Laplace-Beltrami operator and exact solutions for branes

TL;DR

This paper introduces a novel method for deriving exact solutions to nonlinear p-brane equations in Minkowski space by employing specific initial value constraints, expanding the analytical tools available for brane dynamics.

Contribution

It presents a new approach using initial value constraints to find exact solutions of nonlinear p-brane equations, including two specific solution sets.

Findings

Constraints lead to two sets of exact solutions.

The approach simplifies solving nonlinear p-brane equations.

Provides explicit solutions for different initial conditions.

Abstract

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.