The Second Painlevé Equation in the Large-Parameter Limit I: Local Asymptotic Analysis

1997/10/24 by Nalini Joshi, Joshi, Nalini
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9710022

30 pages in LaTeX2e. Submitted

arxiv created 1997/10/24 · arxiv updated 2009/11/30

Abstract

In this paper, we find all possible asymptotic behaviours of the solutions of the second Painlevé equation y''=2y³+xy +α as the parameter α→∞ in the local region x≪α^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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