Inversion of the linearized Korteweg-de Vries equation at the multisoliton solutions

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 \(\Cal W\) 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.

Authors and Affiliations

1. Universität Stuttgart, 70569 Stuttgart, Germany, , , , , , DE

   M. Hărăguş-Courcelle

2. University of Minnesota, Minneapolis 55455, USA, (Fax: 612-626-2017), , , , , , US

   D. H. Sattinger

Received: January 7, 1996

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