Klein-Gordon equation for a particle in brane model
  Brane model of universe is considered for free particle. Conservation laws on the brane are obtained using the symmetry properties of the brane. Equation of motion is derived for a particle using variation principle from these conservation laws. This equation includes terms accounting the variation of brane radius. Its solution is obtained at some approximations and dispersion relation for a particle is derived. 
S. N. Andrianov, R. A.Daishev, S. M. Kozyrev
gr-qc