The Radius of Convergence and the Well-Posedness of the Painlevé Expansions of the Korteweg-deVries equation

Abstract

In this paper we obtain explicit lower bounds for the radius of convergence of the Painlevé expansions of the Korteweg-de-Vries equation around a movable singularity manifold ${\Cal S}$ in terms of the sup norms of the arbitrary functions involved. We use this estimate to prove the well-posedness of the singular Cauchy problem on ${\Cal S}$ in the form of continuous dependence of the meromorphic solution on the arbitrary data.

9 pages in AMSTeX, to appear \textit{Nonlinearity}

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