The Painlevé Connection Problem: An Asymptotic Approach. I
The connection problem for the first and second Painlevé equations is the problem of relating the asymptotic behavior of a solution on a path of approach to infinity (in the complex plane of the independent variable) to those along another such path. A direct natural asymptotic method of solving this problem is described in detail in this paper. In particular, a uniformly valid description of the general (two‐complex‐parameter) asymptotic behaviors—given to leading order by elliptic functions—is derived by a generalization of the multiple‐scales method.
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Document Type: Research Article
Publication date: May 1, 1992