dorsal/arxiv
View SchemaA Local Asymptotic Analysis of the First Discrete Painlev\'e Equation as the Discrete Independent Variable Approaches Infinity
| Authors | Nalini Joshi |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9607006 |
| URL | https://arxiv.org/abs/solv-int/9607006 |
Abstract
The first discrete Painlev\'e equation (dPI), which appears in a model of quantum gravity, is an integrable nonlinear nonautonomous difference equation which yields the well known first Painlev\'e equation (PI) in a continuum limit. The asymptotic study of its solutions as the discrete time-step $n\to\infty$ is important both for physical application and for checking the accuracy of its role as a numerical discretization of PI. Here we show that the asymptotic analysis carried out by Boutroux (1913) for PI as its independent variable approaches infinity can also be achieved for dPI as its discrete independent variable approaches the same limit.
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"abstract": "The first discrete Painlev\\\u0027e equation (dPI), which appears in a model of\nquantum gravity, is an integrable nonlinear nonautonomous difference equation\nwhich yields the well known first Painlev\\\u0027e equation (PI) in a continuum\nlimit. The asymptotic study of its solutions as the discrete time-step\n$n\\to\\infty$ is important both for physical application and for checking the\naccuracy of its role as a numerical discretization of PI. Here we show that the\nasymptotic analysis carried out by Boutroux (1913) for PI as its independent\nvariable approaches infinity can also be achieved for dPI as its discrete\nindependent variable approaches the same limit.",
"arxiv_id": "solv-int/9607006",
"authors": [
"Nalini Joshi"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "A Local Asymptotic Analysis of the First Discrete Painlev\\\u0027e Equation as the Discrete Independent Variable Approaches Infinity",
"url": "https://arxiv.org/abs/solv-int/9607006"
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