dorsal/arxiv
View SchemaThe Second Painlev\'e Equation in the Large-Parameter Limit I: Local Asymptotic Analysis
| Authors | Nalini Joshi |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9710022 |
| URL | https://arxiv.org/abs/solv-int/9710022 |
Abstract
In this paper, we find all possible asymptotic behaviours of the solutions of the second Painlev\'e equation $y''=2y^3+xy +\alpha$ as the parameter $\alpha\to\infty$ in the local region $x\ll\alpha^{2/3}$. We prove that these are asymptotic behaviours by finding explicit error bounds. Moreover, we show that they are connected and complete in the sense that they correspond to all possible values of initial data given at a point in the local region.
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"abstract": "In this paper, we find all possible asymptotic behaviours of the solutions of\nthe second Painlev\\\u0027e equation $y\u0027\u0027=2y^3+xy +\\alpha$ as the parameter\n$\\alpha\\to\\infty$ in the local region $x\\ll\\alpha^{2/3}$. We prove that these\nare asymptotic behaviours by finding explicit error bounds. Moreover, we show\nthat they are connected and complete in the sense that they correspond to all\npossible values of initial data given at a point in the local region.",
"arxiv_id": "solv-int/9710022",
"authors": [
"Nalini Joshi"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "The Second Painlev\\\u0027e Equation in the Large-Parameter Limit I: Local Asymptotic Analysis",
"url": "https://arxiv.org/abs/solv-int/9710022"
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