dorsal/arxiv
View SchemaThe Radius of Convergence and the Well-Posedness of the Painlev\'e Expansions of the Korteweg-deVries equation
| Authors | Nalini Joshi, Gopala K. Srinivasan |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9607007 |
| URL | https://arxiv.org/abs/solv-int/9607007 |
| DOI | 10.1088/0951-7715/10/1/005 |
Abstract
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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"abstract": "In this paper we obtain explicit lower bounds for the radius of convergence\nof the Painlev\\\u0027e expansions of the Korteweg-de-Vries equation around a movable\nsingularity manifold ${\\Cal S}$ in terms of the sup norms of the arbitrary\nfunctions involved. We use this estimate to prove the well-posedness of the\nsingular Cauchy problem on ${\\Cal S}$ in the form of continuous dependence of\nthe meromorphic solution on the arbitrary data.",
"arxiv_id": "solv-int/9607007",
"authors": [
"Nalini Joshi",
"Gopala K. Srinivasan"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0951-7715/10/1/005",
"title": "The Radius of Convergence and the Well-Posedness of the Painlev\\\u0027e Expansions of the Korteweg-deVries equation",
"url": "https://arxiv.org/abs/solv-int/9607007"
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