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}
}
Comments
20 pages