| Numéro |
J. Phys. I France
Volume 2, Numéro 9, September 1992
|
|
|---|---|---|
| Page(s) | 1721 - 1729 | |
| DOI | https://doi.org/10.1051/jp1:1992240 | |
DOI: 10.1051/jp1:1992240
J. Phys. I France 2 (1992) 1721-1729
C.E. Saclay, F-91191 Gif-sur-Yvette Cedex, France
© Les Editions de Physique 1992
J. Phys. I France 2 (1992) 1721-1729
A non-linear differential equation and a Fredholm determinant
M.L. MehtaC.E. Saclay, F-91191 Gif-sur-Yvette Cedex, France
(Received 4 March 1992, accepted in final form 5 June 1992)
Abstract
In several branches of mathematical physics one comes across the Fredholm determinant of the kernel
on the finite interval (
-t,t). Jimbo, Miwa, Mori and Sato derived a
non-linear differential equation for it. We reinvestigate this problem, find five equations
satisfied by three functions
A(t),
B(t) and
S(t) related to this Fredholm determinant, and as
a consequence deduce the differential equation of Jimbo, Miwa, Mori and Sato.
© Les Editions de Physique 1992