Existence and Uniqueness of Tronquée Solutions of the Third and Fourth Painlevé Equations
arXiv:1306.1317 · doi:10.1088/0951-7715/27/2/171
Abstract
It is well-known that the first and second Painlevé equations admit solutions characterised by divergent asymptotic expansions near infinity in specified sectors of the complex plane. Such solutions are pole-free in these sectors and called tronquée solutions by Boutroux. In this paper, we show that similar solutions exist for the third and fourth Painlevé equations as well.
20 pages