J. Phys. I France 2 (1992) 1721-1729
A non-linear differential equation and a Fredholm determinantM.L. Mehta
C.E. Saclay, F-91191 Gif-sur-Yvette Cedex, France
(Received 4 March 1992, accepted in final form 5 June 1992)
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