  We show that collective dynamics of a curved domain wall in a
(3+1)-dimensional relativistic scalar field model is represented by Nambu-Goto
membrane and (2+1)-dimensional scalar fields defined on the worldsheet of the
membrane. Our argument is based on a recently proposed by us version of the
expansion in the width. Derivation of the expansion is significantly
reformulated for the present purpose. Third and fourth order corrections to the
domain wall solution are considered. We also derive an equation of motion for
the core of the domain wall. Without the (2+1)-dimensional scalar fields this
equation would be nonlocal.
