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

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

1996-07-23

arxiv.org/abs/solv-int/9607007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1088/0951-7715/10/1/005

In this paper we obtain explicit lower bounds for the radius of convergence of the Painlev\'e 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.

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