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arXiv · 1306.1317

Existence and Uniqueness of Tronquée Solutions of the Third and Fourth Painlevé Equations

Yu Lin·Dan Dai·Pieter Tibboel
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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.

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Yu Lin, Dan Dai, Pieter Tibboel. 2013-06-06. Existence and Uniqueness of Tronquée Solutions of the Third and Fourth Painlevé Equations. https://doi.org/10.1088/0951-7715%2F27%2F2%2F171

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