The Second Painlevé Equation in the Large-parameter Limit I: Local Asymptotic Analysis
In this article, we find all possible asymptotic behaviors of the solutions of the second Painlevé equation y″=2y3+xy+α as the parameter α→∞ in the local region x≪α2/3. We prove that these are asymptotic behaviors 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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Document Type: Original Article
Affiliations: University of Adelaide
Publication date: May 1, 1999