Why is my rational Painlev\'e V solution not unique?
Exactly Solvable and Integrable Systems
2023-07-18 v1 Mathematical Physics
math.MP
Abstract
Under special conditions the Painlev\'e V equation has more than one rational solution solving it with the same parameters. In the setting of formalism that identifies points on orbits of the fundamental shift operators of affine Weyl group with rational solutions we derive conditions for such non-uniqueness to occur. We identify the seed solutions from which the non-unique solutions are generated and put forward a method to systematically obtain their closed expressions from the underlying seed solutions.
Cite
@article{arxiv.2307.07825,
title = {Why is my rational Painlev\'e V solution not unique?},
author = {H. Aratyn and J. F. Gomes and G. V. Lobo and A. H. Zimerman},
journal= {arXiv preprint arXiv:2307.07825},
year = {2023}
}
Comments
20 pages