Evolution of the D3-brane for dynamical embeddings
  The Dirac-Born-Infeld (DBI) action of the 3-dimensional brane for its dynamical embeddings and the gauge fields has been studied. The evolution of both the D3-brane and the ambient space has been obtained. For the special constraint put on the transverse coordinates a family of the contracting and expanding spaces has been found. 
Pawel Gusin, Jerzy Warczewski