dorsal/arxiv
View SchemaComplex Blow-Up in Burgers' Equation: an Iterative Approach
| Authors | Nalini Joshi, Johannes A. Petersen |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9610013 |
| URL | https://arxiv.org/abs/solv-int/9610013 |
Abstract
We show that for a given holomorphic noncharacteristic surface S in two-dimensional complex space, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlev\'e test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.
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"date_created": "2026-03-02T18:02:51.345000Z",
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"abstract": "We show that for a given holomorphic noncharacteristic surface S in\ntwo-dimensional complex space, and a given holomorphic function on S, there\nexists a unique meromorphic solution of Burgers\u0027 equation which blows up on S.\nThis proves the convergence of the formal Laurent series expansion found by the\nPainlev\\\u0027e test. The method used is an adaptation of Nirenberg\u0027s iterative\nproof of the abstract Cauchy-Kowalevski theorem.",
"arxiv_id": "solv-int/9610013",
"authors": [
"Nalini Joshi",
"Johannes A. Petersen"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Complex Blow-Up in Burgers\u0027 Equation: an Iterative Approach",
"url": "https://arxiv.org/abs/solv-int/9610013"
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