  Uniform estimates for the decay structure of the $n$-soliton solution of the
Korteweg-deVries equation are obtained. The KdV equation, linearized at the
$n$-soliton solution is investigated in a class $\WW$ consisting of sums of
travelling waves plus an exponentially decaying residual term. An analog of the
kernel of the time-independent equation is proposed, leading to solvability
conditions on the inhomogeneous term. Estimates on the inversion of the
linearized KdV equation at the $n$-soliton are obtained.
