Special relations for continuous and discrete Painleve equations

Citation
A. Ramani et al., Special relations for continuous and discrete Painleve equations, J PHYS A, 33(44), 2000, pp. L415-L421
Citations number
14
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
33
Issue
44
Year of publication
2000
Pages
L415 - L421
Database
ISI
SICI code
0305-4470(20001110)33:44<L415:SRFCAD>2.0.ZU;2-G
Abstract
We investigate a relation between solutions of the Painleve II equation cor responding to values of the parameter of P-II which cannot be connected thr ough a Schlesinger transformation, which was first derived by Gambler Here we present the discrete analogue of this relation, relating the discrete P- II to the alternate d-P-II. The latter turns out to be a consequence of a q uadratic relation existing between two different families of solutions of P -V. A q-discrete analogue of the latter relation is also presented.