UCL logo

UCL Discovery

UCL home » Library Services » Electronic resources » UCL Discovery

The Coalescence Limit of the Second PainlevÉ Equation

Halburd, R; Joshi, N; The Coalescence Limit of the Second PainlevÉ Equation. Stud. Appl. Math. , 97 pp. 1-15.

Full text not available from this repository.


In this paper, we study a well known asymptotic limit in which the second Painlev\'e equation (P_II) becomes the first Painlev\'e equation (P_I). The limit preserves the Painlev\'e property (i.e. that all movable singularities of all solutions are poles). Indeed it has been commonly accepted that the movable simple poles of opposite residue of the generic solution of P_{II} must coalesce in the limit to become movable double poles of the solutions of P_I, even though the limit naively carried out on the Laurent expansion of any solution of P_{II} makes no sense. Here we show rigorously that a coalescence of poles occurs. Moreover we show that locally all analytic solutions of P_I arise as limits of solutions of P_{II}.

Type: Article
Title: The Coalescence Limit of the Second PainlevÉ Equation
Additional information: 16 pages in LaTeX (1 figure included)
Keywords: solv-int, solv-int, nlin.SI
URI: http://discovery.ucl.ac.uk/id/eprint/167019
Downloads since deposit
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item