English

Existence and Uniqueness of Tronqu\'ee Solutions of the Third and Fourth Painlev\'e Equations

Classical Analysis and ODEs 2015-06-16 v1

Abstract

It is well-known that the first and second Painlev\'e 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 tronqu\'ee solutions by Boutroux. In this paper, we show that similar solutions exist for the third and fourth Painlev\'e equations as well.

Keywords

Cite

@article{arxiv.1306.1317,
  title  = {Existence and Uniqueness of Tronqu\'ee Solutions of the Third and Fourth Painlev\'e Equations},
  author = {Yu Lin and Dan Dai and Pieter Tibboel},
  journal= {arXiv preprint arXiv:1306.1317},
  year   = {2015}
}

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20 pages