  We present a formalism for computing the higher-order corrections to the
worldvolume action of a co-dimension one kink soliton embedded in
five-dimensional heterotic M-theory. The geometry of heterotic M-theory, as
well as the effective theory which describes a five-brane wrapping a
holomorphic curve by a topological kink in a scalar field, is reviewed. Using
this formalism, the explicit worldvolume action is computed to second order in
two expansion parameters--one describing the "warp" of the heterotic geometry
and the second the fluctuation length of the soliton hypersurface. The result
is expressed in terms of the trace of the extrinsic curvature and the intrinsic
curvature scalar.
