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Uniform estimates for the decay structure of the n-soliton solution of the KortewegdeVries equation are obtained. The KdV equation, linearized at the n-soliton solution is investigated in a class W 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. Mathematics Subject Classification (1991). 35Q51, 35Q53.

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