Inversion of the linearized Korteweg-deVries equation at the multi-soliton solutions
arXiv:solv-int/9808014 · doi:10.1007/s000000050101
Abstract
Uniform estimates for the decay structure of the -soliton solution of the Korteweg-deVries equation are obtained. The KdV equation, linearized at the -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 -soliton are obtained.
39 pages, 1 figure
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